Would competitive chess be better with one allowed take-back per turn?
So after your opponent makes a move, you would be able to undo your opponent's move and your move before that.
You would be allowed at most one take-back per turn.
Would this improve competitive chess?
What happens with the time that was spent on the undid move? Is it lost time, or added back to the clock? If the latter, how would you avoid abusing the undo to gain time? (E.g. think 5 minutes on a move, undo it, and then do it again, but this time in 2 seconds)
Not at all, but refer to the Polgar-Kasparov where Garry Kasparov swore he did not take his hand off the piece, and the next day after Judit Polgar had looked at the film, she blistered his ears. There are enough cheating without adding more ways.
It would make competitive chess even more draw-ish. It is much easier to see when you accidentally get into a losing position than when you miss a winning idea. So the take back would be used defensively.