Yeah leaverbuster will punish you for having bad internet if you often quit because of ping issues. This is as it should be. League is a game that requires 10 people to commit their time for half an hour or more or the game won't be enjoyable. If you can't commit to a game because your system isn't set up for it then don't promise your team that you'll be there. You're ruining the game for 9 other players.
I've had bad internet it the past, and I didn't play much league because of it. When I did, I would hop into a custom game and make sure everything was running fine for a bit before going into a matchmade game. I know how you feel, it sucks, but there's nothing you can do.