Undo moves
I think OP is talking about mouse slips. Some other sites allow a player to propose a takeback for an obvious mouseslip and the opponent can agree, if they want. Some players will offer a draw if they make an obvious mouseslip in a drawn/equal position. Obviously the opponent can agree if they want or continue playing if they don't. I like the idea of proposed takebacks; if the person agrees, the move is undone. If not, the game continues. I see no harm
Considering the number of "rematch" topics in the forum I can imagine how many heated debates will be generated by "takeback" option.

I believe the only way you can do this is in an unrated daily game. Last I checked, it gave you an option to allow requested takebacks while setting up the game. But not in live chess.
I think the "etiquette" is that you should grant the takeback if it's a clear and unmistakable mouseslip, unless both sides are very low on time and mouseslips are to be expected. I could understand someone saying no takebacks. People win due to mouseslips and lose due to mouseslips. In the end it probably balances out
On other sites, I only grant the takeback/accept the draw if:
1) obvious mouseslip AND
2) position is equal or worse for me (for taking the draw). If I'm winning I don't care if you mouseslip, I'm not giving a draw, but I might grant a takeback in such a position

This is an interesting idea, but in my opinion it just takes the feeling of "serious business" away.

Me and a friend used to play some games here when we were about 1200:s, when someone blundered we kind of repeated the moves so we could make another move than the blunder

I think they should make it like in playchess.com, you can offer the opponent to undo their last move, but you can not ask to undo your own move.
Sometimes you are having a really interesting game, and then suddenly the opponent makes some huge blunder (or maybe it was a mouse-slip) and the game ends.
You can offer him to undo his move so he makes something better and the game continues.
In a game that is really exciting I prefer to win (or to lose) because of a beautiful combination, not because of some really huge mistake (like giving the queen away).
chess.com should have a request to undo a move, and if the both players are agree should be done, this are for the unintentional clicks, or how I call it miss click :v