I am interested in this post.
I always thought that it was bad because our moves are never surprising for us.
i pick a side and dont turn the board. play as the opponent from your side, but try hard to make the best moves. and of course try out different lines and see where they go. i go so far as to write them down in a game book and make notes and variations. you'd be surprised what you miss. follow the theory, the lines and play them out, pick the best one and try to out do yourself. the results i end up with are usually bonkers games where "black" wins. i guess i play harder as black and i'm learned to see the threats from the correct persepective because i dont move the board. i just played one where white was up a rook knight to rook and black sacrificed the rook to promote a pawn and came back. the beauty of the game is even when you play the best you can there are many angles and solutions you never have a firm hold because its about resource management. you can easily have a lot of fun trying to out do yourself if you really try to make the best move each time. its a fun way for me to practice when i'm not in the mood to risk points online.
They should do it. when you play chess.com, you play on a device, they should add it so two players can play on one device when the other doesn't have their own device