That's a pretty negative idea don't you think? Not just bad people mess up is just wrong and there is value if you are willing to play on if your better you should prove it by oh I dunno actually playing through an entire game? (you should be able to win it being up by so much of course so why not play on) I'd surrender for sure if I lost my queen but my opponent should have no trouble mating me if they want the win, a mercy rule just take the fun out of it and a player isn't humiliated, its their choice to resign or play on, its much more humiliating if they lose a queen and are immediately notified that their opponent is the better human and they have no chance to improve the position or just their skills in general so why even try to play chess. Mercy rule is for matches that are clearly won but would take too long to finish and in that case stick to rapid if you think your opponent is going out of their way to waste your time. At that point they are just rude, but its usually not the case and they usually do resign when down by a queen, just saying they usually not a diabolical person if they want to play on.
No. I respectfully disagree. Negative would be to allow noxious behavior to continue. Chess is a board game. Board games were invented to improve social cohesion not to encourage all manner of misbehavior.
As to "proving it", invoke the mercy rule and it is automatically proven. If one claims victory by the mercy rule then it is perfectly legitimate because the mercy rule is a rule. No different than castling or capturing a pawn en passant.
Being a better human isn't about inflicting or enduring abusive crap. A better human says, "It looks like I blundered. Set'em up again."
Playing on to supposedly learn something? Plug the pgn into Arena or some other suitable platform and go from there. Let your opponent get on with his life.
The mercy rule doesn't have to be a hard forfeit. Maybe the losing side can ask for 5 more moves. Maybe it isn't invoked. Like a draw by threefold repetition must be claimed, the mercy rule would have to be actively invoked to operate.
I understand, I wouldn't want to wait around playing a game I've already won either. I just see a lot of people new to the games at low levels who don't fully understand why they should resign yet getting upset when their opponent claims victory, and leaves the lobby and they are stuck wishing they had a chance to redeem themselves. At higher levels people wouldn't mind but it may cause too much frustration for new players. Maybe a mercy function could be available in games where both players are above a certain level? or in time controls longer than blitz especially. That would just make sure there are less hard feelings because I know when new players are faced with someone demanding that they resign it can just make them give up on chess or make them salty etc. Time if more of an annoyance for strong players and if they are down by a queen they will know the game is lost anyway so mercy rule should be fine for them. It just has to be implemented in a way that is fair and players can agree with. I like the idea of the losing side requesting a limited amount of extra moves if they truly think they have a chance. Or they simply get 5 more moves to regain material before the other player is awarded the win. Maybe the computer gives the player a 'claim win by mercy rule' option after their opponent is down by a certain score for say 5 moves in a row. I just want people to agree with it so when I use the rule I don't get a whole bunch of 'u suk/to scared to play on' crap in the chat (not that it hurts me but they clearly are upset), Id rather exchange a nice gg and like you said set em up again, or get on with life. And definitely notify incoming players to the website that a mercy rule option is in effect so they can expect it and accept that it is a valid loss. So I actually like the idea but I think we can both agree would need to be implemented justly.
I guess we begginers should take the GM's advice 
For lower rated players against other low-rated players, yes, definitely play until the end in tournaments because your opponent might make a mistake. Here's a recent game I played; yes, I was careless, but a lot of times when you think you've won, you just start to make silly mistakes (hence my qualifier on low-rated players).