@DY If there is a decent argument, feel free to make it.
Done. As far as being obligatory, we pasken not, but it’s a big sugya, and in fact, though not requiring it, the Mishnah Berurah praises the practice if it doesn’t interfere with keeping the zmanim. (See below.)
There’s also a very widespread practice to toivel before the Yomim Noraim and Yomim Tovim.
