ItcheSrulik
i also agree that function is not based on kavanah, and that the beged doesn’t need lishmah. But even so, our tallis katan has no function, since we do not wear them as a shirt, or as an undershirt.
But i’d agree with you that tzitzis that functions as an undershirt has a function, although i do not know if that is the function of a ksus yoim. That would be another shailah.
(i also do not know if there are other reasons why not to wear such a tallis katan. Apparently it is not widespread practice in the ‘yeshiva world’, to wear such a tallis katan. the reason for this, if any, i do not know.)