If dorfs stand on the clothes stockpile picking up clothes, they then have a moment to decide what to do, and one such action is to drop some more clothes where they stand.
Use a separate stockpile for each type of new clothing. xRobesx that get dropped in the shoe stockpile won't be accepted. You'll also be able to tell what you're running low on.
I've actually found it LESS cumbersome to get rid of junk in cabinets than things strewn all over the floor. DFHack's "cleanowned scattered x" takes both, and if you're down to manual management 't' on a cabinet and dumping each item is less work than 'k', move around, and 'd'ump each item.
But you're giving them extra capacity to store their junk. Once they run out of floor tiles to store things on, they'll just leave their clothing about the fort, where it'll eventually be dragged to the worn stockpile. You can put blank refuse stockpiles in their rooms (but not on furniture) to help the strewn clothing decay (only worth it if you have a bunch of open space in the rooms.)
If you have DFHack, you don't have a problem with sorting worn clothing. If you're playing without, it's easier to dump stuff from the stocks screen than use 't' on 100+ cabinets all over your fort. That is, assuming you
can actually dump the owned items. To the best of my knowledge, you can't dump owned clothing, and they'll never lose ownership while in the room/cabinet unless forbidden for about a month (which means extra work and monitoring.)