Should I allow takebacks?

When I was very young and I was playing with my father, I've been ending up losing almost everytime, but we always took back one move (before checkmate), only to see if there's something to do in that position.
I guess this feature is good in some situations (casual games), when you want to see if you can win if you haven't done that particular blunder (perhaps you are playing with a friend or something), but not in the rated ones, that's just silly.

A win of say 10 rating points because of a blunder of the opponent does not mean that your rating will be 10 point higher for eternity. Winning or losing single games has no influence on your rating - your rating will follow your ability. If you enjoy a game and can give the opponent a takeback, you might learn something. -you will both be winners independent on the outcome of the game.
A quick win because the opponent blunders the queen might give you a sense of joy, but you will not learn anything and because it happens rarely it will not boost your rating.
Try in a periode to give as many takebacks as you possible can and then switch to playing like jerk - see if you can tell on your rating graph.

Hear hear.

@hpekristiansen If your opponent blunders his queen early on, you still learn something, even if it isn't as much as from a longer game (for example, it will reinforce the rule of thumb to not move the queen too early in general, or that a specific square or line is dangerous to move on in that particular opening).

No, virtual points are not important. But one's mindset is. I believe that the attitude "meh, when blunders happen, they can be annulled", when exaggerated, impedes you in thinking the hardest you can before making a (final!) decision. A takeback every now an then (in situations where it's obvious that it really was just a mouse slip) is okay. But I would not grant it every single time when asked, that's just not good for one's fighting spirit.

No taksies backsies

What‘s the name of game: takebackgammon?

I once gave a Diamond ring to lady friend. I asked to take it back, saying the engagement is off. She quickly let me know what a fool I was.

Things you cannot take back:
- a stone after is is thrown
- an opportunity once it is missed
- time once it has passed
- a move once it is played.

@ProfDrHack I would not grant two takebacks in a row(some players do try). A line is just as bad or good after one takeback that saves a blunder.
You write that it is bad to be in the receiving end of a takeback, as it can lull you into a sense that nothing matters as everthing can be undone. That is not true as many players will not grant you the takeback, so you really need to play every move as if it is final.

there are few topics i am so passionate about...
takebacks should not be honored under any circumstances. everyone needs to be held accountable for their actions and if you allow such actions you are an enabler and i hope bad things happen to you. the sooner and more often people are held accountable for their actions the more likely they are to change; this kind of change is good.
a mouse slip is a terrible excuse, if the person put forth more effort they should never have one to begin with. if there is a pattern the person may want to change how they move pieces to click and drop rather then click and drag.

one of the few features i wish was never a part of lichess.

i sometime enjoy allowing a takeback only to keep capturing or playing the winning move. for this to work you needed to have played the winning move before the takeback request. also need to make sure they did not request 2 takebacks. i understand this is immature and likely persuades the player into thinking i am the problem, thus skipping the self reflection process. the person feeling entitled to have a takeback honored likely does not self reflect much; that is what i tell myself to help me sleep at night.

lichess please remove this feature.