My argument is that if Tzitzis is like Shaatnez then the underlying Beged (article of clothing) has to have some positive purpose of wearing, separate from being a vehicle for fulfilling the mitzvah of Tzitzis.
Besides protection from sun or cold clothing can be worn:
a) for style if the Beged is visible;
b) absorb sweat;
c) cover nakedness;
d) support other clothing;
e) depict your favorite cartoon character or baseball player (even if not seen by others).
Other purposes that would or may not qualify include:
f) transporting the item (such as on Shabbos);
g) selling the item such as the Shatnez (wool linen mixture) to non Jews who do not have this prohibition;
h) show mourning such as Mordechai did when Haman issued his decree against us, and the Neturei Karta on Yom Ha-atzmaut; and
i) inflict pain on oneself as some non Jewish religious sects do.