It’s objectively harder to play a defense position on the off side. There are about a bazillion interviews with coaches and players to verify that. Everything changes — pucks come up the boards at an awkward angle to your stick, you can’t see the entire ice while you’re puckhandling, you turn your back to the wall and invite a boarding situation every time you dump it in, you’re in a backhand position coming around your own net for a breakout, you’ve got to have an extra step defensively or a winger will blow right by you, you lose leverage on net-front battles and board scrums. Nearly everything other than the act of shooting the puck is harder.
This used to not matter as much, as long as you could find a very talented player to do it. But the game is becoming too split-second reactive. A guy who bobbles the puck even slightly at the point is going to either get steamrolled into the boards or turn it over for a high quality chance in the other direction. The split-second margin of error is gone, and so we’re seeing fewer coaches take that chance with every passing season.
Given that the majority of players, and the majority of quality defenders, are left handed, we’ll still occasionally see the odd LHD playing the right side. But moving an RHD (especially one with mediocre puck skills) to the left just isn’t going to happen. That’s not a matter of coaches being picky, it’s simply not a viable option in this league anymore.