Much of this is based on a 2016 article by Dr. Ari Greenspan, Dr. Ari Zivotvsky and Yosef Zivotovsky, published in the memorial series Mesorah le-Yosef, pp. 77-85, titled אכילת חגבים לבני אשכנז לדעת הרב יוסף קאפח (The Consumption of Locusts by Ashkenazim in the Perspective of R. Yosef Qafih). In light of Ari Greenspan's 2012 participation here on the forum, I wonder if @msh210 your question prompted the composition of their essay.
In the essay it is recorded that R. Yosef Qafih wrote a letter (p. 80) to Ari Greenspan as follows:
כבר פרסמתי רבות בענין הארבה, ולדעתי כיון שאין לשאר עדות מסורת בהן
לאסור, אלא אין להן מסורת לאכלן כי לא הכירום. יכולים הם לסמוך על מסורת
אמת נפוצה מאז משה רבנו ולאכלם וכבר פרסם ד"ר זהר עמר חוברת בהוצאת בר
אילן הארבה ואכילתו במסורת ישראל ושם הפנה לפרסומי על הארבה בכל הכבוד
I have already publicized many times regarding the matter of locusts
and in my opinion since the rest of the ‘Edoth do not have a mesorah
to prohibit them, rather they simply do not have a mesorah to eat them
because they do not recognize them. They are permitted to rely on a
widespread and authentic/true mesorah since Moshe and to eat them. And
Dr. Zohar Amar already publicized a volume from Bar Ilan Press on the
consumption of locusts among the Jewish people, and there he referred
to my publications on locusts with all due honors.
In the periodical, Modiah, Feb 16, 1959, R. Qafih had earlier written:
ונראה כי גם אלה שלא נהגו לאכול את הארבה יכולים לסמוך עלינו ועל
מסורותינו ולחזור לאוכלה בלי שום פקפוק כ"ש וכ"ש שאין למחות בידי מחזיקי
And so it appears that also those that were not accustomed to eating
locusts are able to rely on us and on our mesorah and to return to
consuming them without any doubt whatsoever and all the more so
certainly not to prevent those who strongly hold onto their received
tradition and mesorah
The Kaf ha-Haim stated (Kaf ha-Haim 85:6):
והרבה מקומות יש בספרד שאוכלים אותו... וכן המנהג בתימן שאוכלין אותו
וא"כ התימנים ההולכים לעיר אחרת או הבאים לדור בירשת"ו מותר לאוכלם ע"פ
המסורת שיש בידם
"There are many places in Sepharad where they are eaten"... and so too
is the custom of Yemen where they eat it and if that is so the
Yemenites that go to a different city or come to Jerusalem may it be
built and ready, it is permitted to eat them on the basis of the
mesorah they possess.
This parallels sentiments about kosher fowl identification expressed in the Shakh Y.D. 85 (as cited in Ari Greenspan's answer above), and Rav Moshe Feinstein in Igeroth Moshe Y.D. 1:34, which are clear in that as long as a species of bird possesses the correct simanim and someone has an active mesorah that it is recognizable as a specific kosher species, then that person may be relied upon and the species may be consumed. However relying upon the name alone is insufficient, as names change across geography/culture/time.
However as regards locusts, R. Yosef Yedid ha-Lewi was of the opinion that explicit identification by name is an additional requirement for transmission of mesorah (Yeme Yosef Bathra, Y.D. 3):
מקובל להם מסורת זה לא אהניא לן עד שיאמרו שכד נמסר להם שמין זה שמו חגב
דאל"כ אולי מה שנמסר להם שאוכלין אותו והוא מין טהור סוברין כהרי"ף
דבסימנים סגי ולא בעינן שנדע שיהיה שמו חגב וכן מדוקדק לשון מרן שכתב או
מסורת ששמו חגב לענין דינא אם נתברר לנו אפילו על פי מסורת הק"ק בני תימן
שהם ממדינה אחרת שזה המין אוכלין אותו והוא שמו חגב אז יש לסמוך בפשיטות
לאוכלו אד אם יעידו סתם שהם מקובל להם שהוא מין טהור ואוכלין אותו אך לא
ידעו ולא נתקבל להם אם שמו חגב או לא אז ודאי אין לסמוך עליהם אך הם מה
שאוכלין אין למחות בידם
The mesorah which is accepted by them is not acceptable until they say
that it was transmitted to them that this species name is “hagav” for
if that isn’t the case perhaps that which was transmitted to them such
that they eat them in reliance that they are a kosher species is based
on the reasoning of the Ri”f that the simanim alone are sufficient and
they do not actually know if its name is hagav, and so if we are
precise in the language of Maran who wrote [the Shulhan Arukh, YD 185]
“or that there is a mesorah that its name is hagav” as regards this
law if it is clarified to us that even if according to the mesorah of
the holy community of Yemenites who are from a different territory
that this is the species and its name is hagav then certainly we may
consume them, however if they generically testify that it is accepted
among them that this is a kosher species and they do not know and did
not receive that its name is hagav or not then certain we may not rely
upon them, however that which they eat we should not prevent them
It seems that according to R. Yedid, that in theory one can recieve a mesorah from Yemenites, however this is with the caveat (based on the SA) that they must also transmit a mesorah that it is known by the name hagav. Without this additional qualifier it is not possible to accept their mesorah, as it may be based solely on simanim. His position does not preclude the possibility therefore of transmitting such a mesorah, it simply establishes an additional required element of such a transmission in order to be effective.
The Mishnah Halakhoth (16:8) wrote similarly:
אבל לסמוך עליהם אנן ועל עדותן א"א לן לסמוך שהרי גם הם אין להם מסורת
שזה הוא הנקרא חגב וכיון שאין להם מסורת שזה נקרא חגב הגם שאוכלין אותו
מ"מ א"א לן לסמוך אקבלתם שהרי צריך להיות במסורת ששמו חגב ואין להם מסורת
However to rely on them and their testimony we should not rely for
they also do not have a mesorah that these locusts are called “hagav”
and since they do not have such a mesorah that what they eat is called
hagav and in any event we should not rely on them since it is
necessary that there be a mesorah that the species is called hagav and
they do not have such a mesorah.
According to this view then, the Yemenites lack a mesorah that the locusts they consume are explicitly known by the name hagav. Presumably this position is open to refutation where Yemenites present themselves as in possession of a mesorah for the name hagav as well (as for example expressed in Teshubhoth Rav Qafih, vol. 1, p. 48).
Rav. S.D. Munk wrote against relying upon the Yemenite mesorah for locusts as follows (Shu"T Peath Sadekha 62):
הדברים ניכרים שאינם בקיאים בהם יפה ובודים להם סימן שלא נזכר בדברי
רז"ל שיש להן צורת חי"ת וגם צריכין טביעות עין יפה לומר זה טהור וזה טמא
והרי רש"י העיד שאין אנו בקיאין
The matter is apparent that they are not fine experts, and they rely
upon a sign which is not mentioned by our rabbis, that it possesses [a
body mark that looks like] the shape of the letter ח and these
impressions require a fine eye to say whether they are kosher or not
and Rashi testified that we are not experts.
What is notable about R. Munk's position here is that he generally finds the Yemenite tradition reliably trustworthy such that for example it may be relied upon as regards ethrogim (ad loc):
ולענ"ד גם אנחנו רשאים לסמוך על מסורת בני תימן
an in my humble opinion we are permitted to rely on the mesorah of the Yemenites
It would seem then that while R. Munk is generally comfortable relying upon a Yemenite mesorah, he desists where their mesorah introduces additional unique species identifiers otherwise unexpressed by rabbinic predecessors. It also seems that he thought that among the Yemenites he was familiar with there were not to be found those proficiently expert in its identification.
[Illustration of the form of the letter ח on thorax of kosher locust from Zohar Amar]
R. Zalman Nehemyah Goldberg takes the most severe approach in prohibiting Ashkenazim from consuming locusts, his position as cited in Shu"T be'Mareh ha-Bezeq is:
מפני שלאשכנזים ישנה מסורת לאסור. והגרז"נ גולדברג הוסיף שאין לאשכנזים
לסמוך על מסורות אחרות על-פי תשו' הרא"ש (שורש כ סי' כ).
Ashkenazim are prohibited from consuming locusts because they have an
active mesorah prohibiting its consumption, and that furthermore
Ashkenazim may not rely upon the mesorah of others, as per the Rosh
In other words, it is not just that Ashkenazim do not have a mesorah for locusts (a deficiency that could be remediated), it's that they have an active mesorah actively prohibiting its consumption, and that furthermore even were this not the case, based on the Rosh they would not be capable of receiving the mesorah from another community.
Ari Greenspan, Ari Zivotovsky and Yosef Zivotovsky discuss how in November/December of 2004 there were some swarms of locusts in Israel. They realized that they had a historic opportunity to organize the last living generation in active possession of a mesorah from Yemen and North Africa to pass it on to the larger community and for perpetuity. The authors note that such assemblies, of a public nature, were convened for example in Frankfurt am Main and Halberstadt in order to publicize the sparrow (דרור) as kosher. They record the following rabbis in participation and attendance: R. Yisrael Sharabi (Chief Rabbi of Petah Tiqwa), R. Aharon Badihi (Chief Rabbi of Ebhen Yehudah), R. 'Azaryah Basis (Chief Rabbi of Rosh ha-'Ayin), R. Hananel Sari, etc. They also note that:
הצלחנו להפתיע את באי הכנס באוסף מכתבים של פוסקים מכל הזרמים והעדות
בדבר כשרות החגבים לאכילה על ידי האשכנזים ואלה שמות כמה מן הרבנים שנטו
להתיר או התירו בפועל לאשכנזים לאכול חגבים שיש להם מסורת הרב יוסף קאפח
זצ"ל הרב יוסף צובירי זצ"ל ויבדל"א הרב שלמה מחפוד הרב יצחק רצאבי שליט"א
הרב יעקב אריאל שליט"א והרב עזרא בצרי שליט"א
We succeeded to amaze those assembled at the gathering with letters
from Poseqim from all streams and communities regarding the
permissibility of the consumption of locusts by Ashkenazim and these
are the names of those that permit in actual practice Ashkenazim to
consume them based on the mesorah of R. Yosef Qafih zs"l, R. Yosef Subiri zs"l,
R. Shelomo Mahpoud, R. Yishaq Rasabi, R. Ya'aqov Ariel, R. Ezra Basri,
While there are certainly detractors of the position, it would seem then that the tide may slowly be turning and that there is more overt/explicit articulation of the view that Ashkenazim may consume locusts in reliance of the Yemenite mesorah. I would however note that the only Ashkenazi individual (listed as) endorsing this view is R. Yaaqov Ariel (Chief Rabbi of Ramat Gan, and while he is widely respected as a poseq in Religious-Zionist circles, it is unlikely that Ashkenazim outside those circles would find his stature to be sufficiently persuasive to shift the dial. It could however open the door to other Ashkenazim where there are natural intersections between the Ashkenazi Haredi world and the Religious Zionist world, eventually paving the way to wider dissemination of the mesorah. This remains to be seen.
The Ashkenazi rabbis that permit its consumption (such as R. Yaaqov Ariel mentioned above and R. Hershel Schachter as noted in the comments) apparently disagree with R. Goldberg that there is a mesorah of actively prohibiting Ashkenazi consumption. Rather they must maintain that Ashkenazim simply lacked a mesorah on its identity, and therefore it can be received from others.