There are a lot of problems that cause people to quit. I don't think there is enough effort put into the product to mitigate these issues, and so it just keeps happening. Here would be my suggestions for improving the current situation:
1.) You are allowed (x) number of quits per (y) time period. After which you have two options:
a.) You can rejoin the match that you quit out of
b.) You must wait until that game finishes to join another game
2.) Stop allowing only one side to have a human goalie
3.) Allow a team to change their uniform once. After such a change, allow the other team (x) number of seconds to adjust their jersey.
4.) Remove RP from drop-ins, or better, base RP on grades during the game and not solely on win/loss. Your performance in game should be how you earn/lose RP and not whether or not you won or lost. This would also fix the issue of your whole team quitting on you.
5.) Stop letting the goalie be continuously pulled during play or offer a vote system when there is a request to pull the goalie.
6.) There needs to be some sort of reputation system for players who join games and don't play their position, constantly go offsides, constantly pull the goalie, try to score in their own net, etc. I'm not sure a vote to kick system is the right choice because it could be abused if a team votes to kick someone just because they aren't as skilled in the game. Maybe force them to go through a tutorial before they can play online again or something after they do this. Maybe also implement some sort of cooldown for joining an online game again for the most egregious players who do this.
7.) Allow reconnects to the game if for some reason you disconnect during play. This should have been added a long time ago.
8.) Smurf accounts are a real thing, and this is where you can lose a ton of RP. I'd like to see the card system return, or maybe some variation of it. If you had to earn those points again in some way, it would make smurfing less effective and might discourage people from doing it. Right now, there is no penalty for doing this. Changing the RP system could make this less meaningful.
9.) When people start leaving the lobby, start searching again for new players, don't just start the game. The old lobby system was better at dealing with this. I don't know why the game isn't smart enough to try to fill as many slots as possible. I get that people can quit after the game launches but maybe offer a reprieve to the quitting mechanism mentioned above if the game launched with (x) number of players and lost (y%) of players before puck drop. You could also offer the option of taking everyone back to the lobby until more people join.
10.) Begin the game right away once (x%) of players have set their status to ready.
11.) Allow players to go to the bench and change their builds during play. Maybe allow a one-time change or once per period. This would mitigate those who wait until the last second to change their builds.
12.) Human goalies should need a certain level before they are able to join a drop-in game. Make them learn to play the position first. This would also stop some people from trolling goalie.
13.) See above number 6 for human goalies who skate out of their net, try to start fights, etc.
14.) Stop letting people use offensive builds on defense and vice-versa.
15.) Allow position switching between periods. If for some reason you lose a d-man or something during play, you should be able to switch back to that during intermission. Or maybe you want to drop back and play defense and let a teammate move up.
There are probably others, but these would be top on my list. A lot of the quitting could be addressed but there needs to be some sort of impediment for trolling. Throwing your hands up in the air and screaming "but what about abuse" is not going to fix this issue and it's been going on for far too long. The people who troll are already abusing the systems in place. I do think the vote to kick could be abused, but there are other options.
I know this is anecdotal, but so many people I know who used to play this game religiously won't even touch it now. With the lack of commitment to address issues that plague this game, to the pre-built loadouts, to the crazy characters on the ice (werewolf, etc.) it's not surprising that people can't readily find games.