Although he does not seem to agree with the full extent of your citation (i.e. that it is an actual duty), Rambam (Hilkhot Tsitsit 3:12) writes that this mitsvah is particularly important, and therefore one should try to perform it:
אף על פי שאין אדם מחוייב לקנות טלית ולהתעטף בה, כדי שיעשה בה ציצית, אין ראוי לאדם חסיד, לפטור עצמו ממצוה זו; אלא לעולם ישתדל להיות עטוף בכסות המחוייבת בציצית, כדי שיקיים מצוה זו. ובשעת התפילה, צריך להיזהר ביותר; גנאי גדול הוא לתלמיד חכמים, שיתפלל והוא אינו עטוף
Even though a person is not required to purchase a tallit and wrap himself in it, so that he [will be obligated] to make tsitsit for it, a pious person should not exempt himself from this mitsvah. Rather, he should always try to be covered with a garment that is required in tsitsit, so that he should fulfill this mitsvah. And during prayer, he needs to be particularly careful with this; it is a great disgrace for a talmid hakhamim to pray without being wrapped.
The next halakha seems to provide the explanation for why this mitsvah is unique in that pious people should try to fulfill it:
לעולם יהא אדם זהיר במצות ציצית, שהרי הכתוב שקלה ותלה בה כל המצוות כולן, שנאמר "וראיתם אותו וזכרתם את כל מצוות ה', ועשיתם אותם" (במדבר טו,לט).
A person should always be careful with the mitsvah of tsitsit, for the verse (Numbers 15:39) states: "And you shall see it, and you will remember all the mitsvot of God, and perform them".
His son Rabbenu Avraham elaborates upon this point in the halakhic portion of his HaMaspik L'Ovdey Hashem:
אין האדם מחויב לקנות כסות ולעשות לה ציצית...אולם..הנה רצוי ומומלץ...[ש]ישתדל לקנות טלית שהיא חייבת בציצית ויעשה בה ציצת, ויהא לובשה תמיד או במרבית זמניו כדי שתושג אצלו תכלית המצוה הנכבדת הזאת שהיא וראיתם אתו וכו
A person is not obligated to purchase a garment and make tsitsit for it...however...it is preferable and encouraged...to make an effort to purchase a tallit which is obligated in tsitsit, and to make tsitsit for it, and to wear it all the time, or much of the time, to achieve the objective of this exalted mitsvah, which is "and you shall see it", etc. [i.e. and you will remember all of God's mitsvot and do them, and you will not stray after your hearts and after your eyes which you lust after, so that you remember and perform all of my mitsvot, and be sanctified to your God]. (Dana's Hebrew translation pp. 270-271).
Similarly, R. Yonah of Girona writes (Sefer HaYirah) that one should make a point of wearing tsitsit since it will remind him of the mitsvot:
ויהיה לו טלית קטן וילבשנו...כי עיקר מצות ציצית לזכרון ללבשו תמיד
And he should have a tallit kattan and wear it...For the root of the mitsvah of tsitsit is as a remembrance, he should always wear it.
This is paraphrased by the Tur (OH 24) who writes:
טוב ונכון להיות כל אדם זהיר וזריז במצות ציצית שיהיה לו בגד קטן מצוייץ שילבש אותו כל היום כי עיקר מצותה על זכירת המצות ובכל שעה ובכל רגע צריך לכך
It is good and proper for every person to be careful and proactive regarding the mitsvah of tsitsit, to have a tallit kattan with tsitsit to wear all day, for the main [purpose] of the mitsvah is to remember the mitsvot, and one needs this every hour and every moment.
This is in turn cited by the Shulhan Arukh (OH 24:1):
וְטוֹב וְנָכוֹן לִהְיוֹת כָּל אָדָם זָהִיר לִלְבֹּשׁ טַלִּית קָטָן כָּל הַיּוֹם, כְּדֵי שֶׁיִּזְכֹּר הַמִּצְוֹת בְּכָל רֶגַע.
It is good and proper for every person to be careful to wear a tallit kattan all day so that he remember the mitsvot all the time
Importantly, neither Rambam, nor Rabbenu Avraham, nor Rabbenu Yonah, nor the Tur, not the Shulhan Arukh encourage making the effort to wear tsitsit because it is a situational mitsvah, such that you would ask about all other situational mitsvot. Rather, they explain that the particular emphasis on this mitsvh, is due to the unique role of this mitsvah; driving us to remember and perform all of the mitsvot.
In a different vein, Maharil writes (Shu"t HaHadashot: 7) that one should wear tsitsit simply because it is a mitsvah and one should pursue mitsvot. He makes clear that one is not obligated to acquire a garment with tsitsit, but that it is good to pursue mitsvot:
אין מחוייב לקנות בת ד' אלא דמצוה להכניס עצמו לכלל חיוב כדילפינן ממשה רבינו ע"ה וכי לאכול (מפיריה) [מפריה] כו'
One is not required to acquire a four cornered garment, but it is a mitsvah to bring oneself into the realm of the mitsvah, as we learn from Moshe [who wanted to enter Israel to perform more mitsvot].