Hope all is well. I recently heard from someone that the classical Brisker Derech is to not wear a Tallis Kotton since, if it's not something which one classically would have worn without Tzitzis, it cannot be considered an actual Begged? I probably butchered the analysis, but clarification on this matter would be very much appreciated.
I am not familiar at all about this practice. what I have heard is that some follow the practice of the Maharm Ruttenberg not to wear tzitzit on shabbos out of the eiruv. The Netziv in his teshuvos Meisiv Dovor discusses the two different reasons given by different talmidim of the Maharam for this practice. Some of the Brisker have a third totally different reason for the practice that since today we don’t have techeilis the tzizit mitzvah is incomplete and the only time the strings of the tzizit are not considered a “masoi” is when the mitzvah is in its complete form.