Are Tzitzis obligated in Tzitzis

Question

According to the Rosh (Moed Katan 3:43), a garment worn solely to absorb sweat is not considered a בגד (with regard to the obligation of מצות קריעה - mournful rending). This principle is invoked by later authorities to exempt four-cornered undershirts from tzitzith (see, e.g., Tekhelet V'Argaman 5, s.v. apikresin, citing Rav Chaim Kanievski; Shu"t Chemdath Tzvi 3:3; and Shevet Miyehudah, Ki Teitzei, cited here). Seemingly, even those who argue, agree that this is because the undershirt does have functional garment benefits (ibid):

Yet, it does not appear that our undershirts are made solely for the purpose of absorbing sweat, for they also serve to provide a degree of warmth in the winter, and a degree of comfort in their touch. Moreover, they are sometimes worn alone, for instance when playing sport–though it stands to reason that this does not give them any great importance, for it is the way of sportsmen to wear ‘undershirts’ alone.

What about a garment worn solely for ritual purposes. For example, if one wraps oneself in an American flag on July 4th, it might be argued that the fact that it is visible gives it a "fashion"-like garment function. But if there was an unusual (hypothetical) custom to hide the flag between one's undershirt and shirt, there would seem to be no garment-like function at all.

Accordingly, why would an otherwise functionless (at least on warm days) traditional tallit katan be obligated in tzitzit? Is the reasoning that a garment functional in winter, is also considered a בגד when worn in summer? Likewise, is a tallit gadol only obligated in tzitzit if simultaneously otherwise functional? (Similarly, would the same reasoning apply with regard to carrying on Shabbos and מצות קריעה?)

Answer 1

Indeed, perhaps a functionless tallit is not obligated in tzitzit. This seems to have been the opinion of R. Avraham Yeshaya Karelitz, at least:

Shilhi Dekayta Siman 8

וכששטחתי את גליונות הספר קמיה מורי הגר"ח קניבסקי שליט"א אמר הגר"ח שגם לדעתו אכן צריכים הנאת לבישה מהציצית וכן מוכח ממנהג החזו"א זצ"ל שהורה שלא לילך בקיץ כציצית מצמר למרות שלדעת חלק מהראשונים דוקא ציצית זו חייבת מדאוריתא בד' כנפות וכנראה דס"ל דכשמתענה מלבישתו אזי חסר בהנאת הבגד ומשו"כ אי"ז בגד הראוי לציצית ואכן מן הראוי לפרסם סימן זה אך יש להדגיש שהדברים אינם מוסכמים ולא בכל עת שרב אכן פטור מדינא מלבישת הציצית

Earlier in the siman he cites other contemporary authorities. Apparently R. Shlomo Zalman Auerbach and R. Chaim Pinchas Scheinberg disagreed, but R. Yosef Shalom Elyashiv agreed that the garment needs to provide some sort of benefit.

Answer 2

Rabbi Jonathan Ziring, in the lecture linked to above by DoubleAA, brings a Machlokes between Rav Aviner, who allows people to wear an Israeli flag without adding Tzitzis, since it has the status of 'clothing for honor', which do not qualify as a beged for tzitzis, and Rav Ariel, who says that if one is wrapped in it (and it would fall under Ituf), you are actually required to put on Tzitzis. However, it seems that it would still be frowned upon to enter into such a situation (both legally and in terms of the honor for such a symbol), and ideally, the corners should be rounded to avoid such an issue.

Others point out some other reasons for leniency, such as that there are not two corners in front and two in back - I personally don't see any reason why if someone is wearing it as a cape (or a tallis), that this leniency would apply, but it would apply if it is simply around their neck and all 4 corners are in the front.