why not mount a row of hooks on the wall right next to the door?

you won't destroy the integrity of the door by mounting a hook on it if you
do it correctly but it's not really something you want to do either. Wall
hooks should be just as useful and it will be much easier to repair the
holes in the wall than in the door if you ever decide to remove it.

I've seen these nicely routered and finished blocks with 3 or so hooks on
them that you can buy at the supermarket for a few dollars.