The reason one would want to do this is to reduce wear on the watch, since the dominant hand is going and doing things the dominant wrist is more likely to be smacked.
This goes double for expensive watches.
Personally, I think it's the opposite. I wear my watch on the wrist of my dominant hand. I've never had a problem; in fact I think you are more likely to pay attention to it and not smack it into things.
I am right-handed and wear my watch on my right wrist as well. I've never ran into any problems doing so, and manipulating buttons on different watches was never a problem either.
You wear your watch on your dominant hand? That feels very unnatural to me. Just manipulating the straps alone seems difficult, so that's a barrier right there...
Not to forget, that most Watches are designed to be worn on the left side. (Position of the Buttons etc.)
Smartwatches are improving here, in displaying a rotated screen, but often even these are asymmetrical designed and thus harder to use on the right arm.
I do as well. Even since I was a kid, wearing watches on the wrist of my non-dominant hand felt unnatural. I have no problem manipulating the strap or buttons on my watches.