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?)