Quit bans can be implemented in destiny, sure. They would preferably be used to deter habitual quitters. Quit too many games in some time frame, get a time out for some period. Continue quitting while on probation, get a more severe quit penalty. Play nice for long enough, you are brought back to normal status.
However, under no circumstances should a quit ban of any duration be placed on a player after leaving a single match. If I'm queuing up for a crucible match and get put in a game down 5k or something, fuck that. I'm gone. Fix your mercy rule system first before punishing players from leaving a terrible experience. Leaving crucible is much more acceptable than leaving a strike since losing is actually a possibility. For strikes, prioritize games in need of 1-2 more players for matches over that of new games. Filling strikes immediately is more important than filling crucible matches that should have just been ended.