On what grounds can rabbis make such pronouncements, tying the hands of all future rabbis, even if conditions should change?
After some digging, I have found that the language of כל ימי עולם ('all the days of the world') comes from a letter that R. Shaul Dowid Sitthon wrote, describing the 1927 ban. To be clear it is not the language of the ban itself. Parts of this letter appear to often be circulated (especially online) as if it actually is from the ban, whereas it is not in fact therefrom.
Here is the text of the letter as transmitted in Devar Shaul, pp. 24-25:
אמר המחבר עוד יש טעם אחר לאסור בנד”ד אף אם היה עשוי עפ"י הדין כמ"ש נהר
מצרים ועצי הלבנון וגאון א' הובא בעתון נקרא "הבאר" מפני כי העיר הזאת
חפשית עד מאד ואיש הישר בעיניו יעשה ואין להם רב שיראו ממנו לא מצד
הממשלה ולא מצד שהוא ממונה לרב מהק"ק יצ"ו וא"כ כל איש אשר חשקה נפשו בבת
נכריה מביאה לביתו ותהי לו לאשה בלי גרות או מביא הדיוטות מן השוק
ומגיירה בפניהם כאשר מצוי כן עתה ויש להם בנים והם פסולין ואומרים
שיגיירו אותם ואם ישאל אותם אדם בפני מה נתגיירתם ישיבו בחציפות מי שמך
וכו' ולמה לך להיות עובר ומתעבר ונשאר עם נכריה ומוליד ממנה בנים וולד
אשה כמוה ונתערבה בנברים ושלחתי פסק”ד שעשיתי ופסק"ד של הגר”א הלוי הנז'
למעלת הרה"ג כמהר"ר יוסף ידיד הלוי הי"ו ראב"ד לעדת החלבים בני אריץ אשר
בעיה"ק ירשות"ו והסכים כדברינו וכתב פסק"ד ארוך ולא הניח זוית ופנה ולא
הדפסתיו משום הוצאות הדפוס ואז פזרתי מודעות שאין לקבל גרים בארגנתינא
עוד כל ימי עולם מכמה טעמים כאשר הסכמנו שלשתנו ואין לפרוץ גדר וכל הפורץ
גדר ישכנו נחש, ושומע לנו ישכון בטח ושאנן מפחד רעה ומו שרוצה להתגייר
יטע לירושת"ו אולי יקבלוהו וציי"מ וימ"ן אמן, כ"ד רועה צאן קדשים בעי"ת
בואינוס אייריס.- הצעיר שאול דוד סתהון ס"ט
The author states: There is additional reason to forbid in this matter
even where it has been done according to the law as is written in
Nahar Misrayim, Asse Lebanon, and as one Gaon wrote in the circular
“HaBe’er”, because this city is very libertine and each person does
what is right in his own eyes and they have no master that they are in
awe of, not due to his authority nor due to his appointment as the Rav
of the Holy Community, and since this is so that any man that lusts
after gentile women, takes her into his home as a wife without having
performed a conversion, or has a conversion performed by unlearned
laypeople in the marketplace such as are found now and they have sons
thereby that are pasul and claim that they have converted them, and if
you ask one of these people before whom they converted they retort
with they answer indolently “what’s your name?” etc. For what should
they go over and live with gentile women, and conceive and have sons
with them, and become mixed up with the gentiles? So I issued a pesaq
din that I made, and a pesaq din of HaGaon R. Ahahron Ha-Lewi
[Goldman] mentioned above, and Morenu HaRav, Rav Yosef Yedid ha-Lewi,
Rosh Ab Beth Din of the Allepan community in Jerusalem, who agreed to
our words and wrote a lengthy pesaq din that considered every angle
though I did not print them here due to the costs of printing, so I
distributed announcements that converts should not be accepted in
Argentina 'all the days of the world' (כל ימי עולם) for many reasons
as we agreed and one should not breach a safeguard and anyone who does
deserves to be bitten by a snake and those who hear us will dwell
securely and not fear evil and one who wishes to convert should go to
Jerusalem where perhaps they will receive him. May the Rock of Israel
save us from error, and may we see from His Torah wonders, Amen.
Shepherd of holy lambs of the City of Buenos Aires – the youth Shaul
Dowid Sitthon, Sepharadi Tahor
As we know (H. Sanhedrin 24:4:), a safeguarding measure may be established by a court according to the needs of the time, though may not establish it in perpetuity. They are to stand as long as the conditions persist and the court deems it necessary. Accordingly, I would say that it is unlikely that the language of כל ימי עולם was actually used in the original ban and that when R. Sitthon describes the ban in his letter he is using hyperbole, that it is figurative language added for strong emphasis and the gravity with which the matter was considered. In light of where we know this text to have come from and the operative halakhah, it would be difficult to maintain that this was ever intended as an actual expiration date or that such language was actually employed in the ban itself.
What is the practical value of such a ban, if candidates can get converted outside the country?
I would ask on the flipside of this, of what value would any enactment be outside of its own jurisdiction? A court cannot enforce something outside of its purview and geography, on both practical and halakhic grounds. I believe the assumption in this particular case especially, is that setting up this impediment will prevent the vast majority of transgressors of this type from sinning. It seems that this was being done as a function of תיאבון (appetite) and where that appetite was curbed by this measure, it was sufficient to produce the communal effect desired. It also opened an avenue for those sincere in their desire to convert by sending them to Jerusalem.
From the comments:
How did that rabbi manage to make his edict stick and extend to all
conversions in Argentina, under any sponsorship?
This ban was issued with the backing of his Ashkenazi colleague R. Aharon Goldman of Qiryath Moshe (Moisés Ville), Argentina. It also had the backing of R. A.Y. Kook (first Ashkenazi Chief Rabbi of British Mandatory Palestine) as well as R. Yosef Yedid (Rosh Ab Beth Din of the Allepan community in Jerusalem). In their letters of support they affirm his authority to do so as a סייג or גדר (presumably with all that such halakhic terms entail) to protect against the Torah's violation.