I have often had many bad moves that I would like to take back, but the app had already recorded them. I had not intended to post them. So I believe that this would be a good idea.
The idea is good, but the only worrying issue is that there will be a small group of players who would probably attempt many takebacks in a game just to distract other players. I strongly believe, however, that a game would probably have one or two takebacks for real reasons such as mouse-slips.
And then we will have the new wave of threads:
"I obviously made a mouse slip here and user1234 didn´t give me a takeback, where is the sportmanship?"
"Should we block people that don´t allow take-backs?"
"I was winning and this loser won just by refusing my take-back!!!!"
...