I have several comments, but also want to state that most of what I play is turn-based so that's the point of view I'm coming from.
I understand why there's no ELO when someone quits the game. For some games it really doesn't matter, but for some it does. I just continued a Can't Stop where someone quit and that certainly didn't make any difference. But I also had a Stone Age where someone quit, not only turning it from a 4-player to a 3-player with no adjustment to rules, but the system still somewhat considered the one guy to be there but just skipped his turn, so the person following him got to be first player twice in a row, really messing with the game. It was certainly not a normal game after that, so why should there be any ELO? (Too bad - I won anyway.)
Maybe in a 2-player game... but quitting is not conceding. To concede means you believe your opponent has won. (And that option exists if they care to do it the proper way.) Just leaving does not necessarily mean they've conceded. I'm not sure what would be a fair way to decide how far along the game has to be before it still counts, and who gets to decide if someone really won. Who gets to decide if they left because they were losing? That might be obvious sometimes, but it's not always, and something else could have happened. And if someone quits early in the game, I see no reason I should get an ELO boost when I never won. (Using it as a penalty is one thing, but using it as a reward for who got left behind?)
I also do not like the idea of banning someone, for the same reason -- stuff happens. I would rather see someone banned due to their
percent of times they've left. Having to leave a game occasionally could be for any reason and shouldn't hurt people. But if you're leaving 20% of your games, that's a different issue.
From what I've seen, the ELO penalty has only been 10 points. I don't know if someone at 1500 doesn't get as penalized and it's mostly noobs who are quitting? I've never seen anything bigger than that, and 10 points is not even worth worrying about. If someone continually does that because they're losing, yes that would affect them over time. But I just don't see that as any great penalty. (I could see the point of applying ELO as though that player had come in last.)
There is also the unfortunate situation that the vast majority of (at least in the case of turn-based) games, the admin does not close it to those with higher percentages of quits or red thumbs. So as long as the admins don't do that, there will be games that person can join, so why should they care? I've already learned not to join those unless I'm the last player and I know who has already accepted. That actually cuts down a fair number of games, but why bother when people so often just don't show up? I'm really just not sure these "penalties" have that much meaning to those players.
But I agree something needs done.
As to the ELO... I've noticed some games get cancelled when someone quits or gets expelled and some don't. I had made the assumption when they're cancelled it's cause it's a game that just won't work with someone gone. I don't know if I'm right about that. But how difficult would it be to take the games in which it would not matter if someone left, in which it would not affect the rest of the game in any way, and unless the players choose to abandon it, go ahead and do ELO? I don't know many games but best examples I can think of are Yahtzee and Can't Stop. Someone leaving those isn't going to hurt the rest of the game or affect how people play. But I bet it would matter for a lot of games, and I don't think ELO should be applied for those, other than the penalty.
(By the way, I do see the difference between an issue with ELO, and just the fact that people quitting isn't much fun, ELO or not. So there's more than one issue involved here.)
I think it's unfair that when you have to expel a player, the game doesn't count to your ELO. Knowing this, sore losers will time out when they are losing instead of honorably quitting the game. In chess or any other game a time out of your opponent is a win for you. Of course, there might be a reason for this I'm missing, so please explain to me 
