Wow. I've never had a issue with self winding while wearing it. I let them stop when not wearing them. I get them going for a few days every few months to keep things loose. I figure that given the infrequent use, issues from wear in a watch winder will exceed issues from sitting.
as above, my watch maker/fixer guy says do not use a watch winder, his logic is, would you leave your car engine running in the driveway so its ready when you want it?
At the current rate of Omega and Rolex service , having them sit idle a bit is just fine.
My pockets aren't deep enough for stupidly expensive watches , but I did have a pretty nice watch with sentimental value ruined by a hack watchmaker ( actually two of them) , so if there was ever a case of you get what you pay for , it may be watch repair.