I believe ICC has this capability....if you make a blunder like you are referring to and wish to take it back for the purposes of continuing a meaningful game (unless you are a beginner and wish to work on mating patterns or winning won positions, etc. all sorts of exceptions) you can click on the "Take Back" button, and it will offer to the opponent to take back your previous move. Therefore, it comes down to your opponent as to whether or not to allow the take back. This feature has worked successfully there, so I don't see why it wouldn't work perfectly fine here.
A reverse sides option would be interesting too.
if there was a takeback option you need your opponents permission, and anyway, it wouldn't be fair.
Take that back!
If there were a takeback option, then it would be almost impossible to win or lose, since you could easily take back a mistake you made, so neither of you would blunder or make any mistake of any kind. You may as well be allowed to use an engine!
Isn't that what the submit button is for on the mobile app?
With a mouse I think it is much less of an issue.