take back in a rated game??

I have to agree: in a rated game there should be no take backs. It teaches discipline. I have no problem learning from my mistakes. What I would suggest is to set aside a private game with the same moves up to that point then let the other player continue the game with a different move.

When you think about it, in GM games it's really no different: one player makes a move that changes the course of the game for better or worse, right?

I guess I look at it as a way to learn a lesson - you can't take back in tournaments so why do it in casual play? It is only one game after all and we have all made those blunders and lost. In the end it all works out anyway so I wouldn't worry about. Another point: I've made a blunder and had my opponent make a blunder later in the game and I ended up with a win. It taught me to never give me up.

MY

This makes a lot of sense and avoids most potential for abuse.

A rated game should allow NO takebacks under any condition.  As Genna Sosonka pointed out, it's an affront to Caissa and an insult to the game of Chess.

In an unrated game.... who cares?

The ICC has an option to request a one or two move takeback, which the opponent must accept.  There is also an option to abort the game, which both people must agree to.  Also, there is the option to adjourn the game, to be resumed at a later date.