WOW, looks impressive! Nice house for your watches!
One day a month? How stupid! You can save the money then.
The function of a winder is to wind automatic watches. You surely don´t need to let it move all day and night, it certainly has a timer and a presetting. So you can program it to run 10 h a day and bidirectional moving, should be enough to keep the watches winded.

Yes, of course it wears them, the movement is running as if you wear the watch all time. But putting them in a drawer doesn´t save a service after some years, it´s the oil which must be replaced. It´s a personal decision to use a winder or not. Some experts say the abrasive wear is too much, other experts say it´s better for the movement to stay in motion.
Some people wear their one and only watch for decades without problems, so for a Swiss movement of high quality and in good condition, with enough oil in the bearings, it shouldn´t be a problem IMHO.
I own just a single winder and almost use it for day/date watches without quickset to keep them up to date when I want to wear them again inner a few days.