You can already do this.
Taking Back A Move - Heresy

I find this a bit ironic since allowing moves to be taken back would probably have the same effect.
Like Ivan has already mentioned, you can already do this.

@OP: Yes, you can specify a take-back game. First, specify that you want the game to be unrated. Then, after expanding all options, you should find a pull-down window that will permit you to create a take-back game.

@OP: On the window that says "This is a rated game," the pull-down menu includes an option to create a take-back game.
Can you find that?
You choose when you choose from the options given for type of game you want to pay - Take Back.
Thank you Ann. I assume that if the option is selected at the start of the game, you can't add it after you've begun? Also, do both players have to agree upfront? If yes, how likely is it that seasoned players will select that option?
Heresy!
I'd rather resign than play a game on mercy*.
*except with friends otb.
I'm not talking about mercy. I'm talking about investing hours in a great challenge - then seeing that challenge come to an abrupt end due to a single mistake. Winning is always nice. But winning against a solid player is always nicer than winning through a fluke error.
They're lying, its done with magic and spells and such.
Ivan, you're confused. When I win it's due to magic and spells.

@OP: Yes, both players must agree. I would guess that relatively few seasoned players will go for a take-back game, but you should be able to find someone to take you up on it.
Settings can't be changed after the start of the game.
Also, beware of one fact that I noticed someone else complain about regarding take-back games: I've heard that either player can postpone checkmate indefinitely, because when one player notices that he's one move from mate, he can simply take back all the moves he'd like, until he's satisfied that he's no longer losing. Then the game takes a different path. As I understand it, this can be done repeatedly, potentially making the game never-ending.
I suspect I will get blow back for this, but I wish Chess.com offered the option to take back a move.
And, really, it is not my dumb moves -- although I make plenty of them -- that I wish could be reversed. It is the moves of the terrific opponents I play.
I love the mental jousting entailed in a close chess match. I make a solid move, my opponent counters with a brilliant move. Back and forth.
Then, just as the match is progressing toward a climatic conclusion, my opponent makes a seriously dumb move. S/he didn't see a piece and loses a queen or other major piece. Poof. All the competitive air goes out of the game.
If I win it is not because I was a better strategist in this particular game. It is because my opponent made one bad move.
I'd happily let my opponent have the move back, if Chess.com would let me. If I win, I want to win a well-faught contest. Not one where my opponent tripped near the finish line.