This game DESPERATELY needs a matchmaking structure.

Rather than focus your efforts on creating a penalty for leaving, why not just build the penalty into a ranked structure?

The main problem with queuing by yourself is the vast skill level differences you receive from the players on your team. I would consider myself to be somewhat experienced, and it seems like every game I get at least one, if not both of the players on my team to be under level 10. So why is someone who hit level 100 within a few weeks of release with over 250 wins total being CONSISTENTLY paired with people that can't even aim properly?

If you take the approach that Realm Royale had, where every season you climb the rankings by placing higher in games. You couldn't actually decrease your rank, but the higher rank you got, the harder it was to actually climb higher and higher. Example, it went from bronze to master. Bronze>Silver>Gold>Plat>Diamond>Master. If you're at Gold 3, and you won a game, you might get enough ranked points to jump from Gold 3 to Gold 1, then the next promotion would be Plat 3. If you place 12th in a game of 100 people, you'd get obviously less ranked points than a win, so it would take longer to grind your rank. But you'd never actually lose the place you were in. 

The first thing I said about the leaver penalty would be, in my opinion, the best way to make staying an incentive. Each match, you cannot leave within the first 3 minutes of the match. Put a visual on screen timer. Make the person who left lose rating.

The worst feeling is dropping into a city, doing your absolute best, you might even be on a kill streak with a good load out. Then your team mate gets downed and even before they get executed they leave the match. This puts a heavy halt on your performance and lessens your chances to win the game. This way, people who leave super fast get sent back down in rating and can't interfere with players who are making an attempt to climb the ranking ladder. If X person has a habbit of leaving the second they get downed, then they will derank to a point that they aren't in anyones way. Sure they will be matched with other players who are lower skill tier and trying to improve, but at least the competition wouldn't be as severe. Low tier player with a horrible team mate (leaves instantly) against a good player, this will never end well for them.

If that person who left instantly without even giving their team mates a chance to clutch the match and get their banner, then they should lose a considerable amount of ranked points. 

So you have a system where the only way you climb rank is doing increasingly better. If you're at one of the highest ranks, you could even make winning game with higher damage rating more points than if you won a game with 3 kills and 400 damage. Only way you'd lose rank is if you left. 

I'm not saying segregate the population, I'm simply divide it up to where the best players are at the top and the worst players are at the bottom. This allows lesser players to improve without having to play against Shroud and the top tiered players get consistently difficult engagements more often.