Personally, what they need to do is flex LP gains/losses by total contribution, with a steep penalty for leavers, on a per game basis instead of avg MMR.
If you go 15/3/12 and win, and your jungler was a 0/8/3 afk farming flamer, he doesn't get as much LP as you, and if you lose under these game circumstances, you lose less than him.
This is very oversimplified, but the general idea is to note contributive factors such as Kill Participation, Vision Score, Objective participation, CS, and whatever it needs to look at to calculate the "deaths per minute" stat in game to keep track of how much exp and gold you feed your enemies) to determine how much of the game you contributed to in the win/loss compared to your other teammates, and math away at it to assign a number out of 100 total points (20LP avg between 5 players, in a perfect world, but literally nothing is perfect, so there will be someone who possibly has a few more than 20 points and a couple people with like 14-18) This would better reflect and reward skilled players, and better reflect and keep down less skilled players and leavers, without completely nuking everything. If you go 0/8/0 afk farm jungler with a vision score of like 8 and no objectives, you're gonna be gaining like 13 points on your win, or losing like 26 on your loss, because you were the lowest contribution to your win, or one of if not the highest contribution to your loss. Leavers just need a stiff -35 regardless of win or loss. >.>
A win is still a win and a loss is still a loss, but it would make immediate sense why your 23/2 mid got more LP than you and your 3/9 top lane did, and would encourage people to focus on playing the damn game instead of playing politics for who won/lost it. The evidence would be plain as day: 0/8/0 with no contribution takes a big hit (which hopefully demotes them) and 9/11/6 whose back broke loses less (and hopefully doesn't get demoted.
15/3/12 with 200+cs at 20 gains more (and hopefully just hit promos) while 3/11/12 gains a bit less, but is still moving up.
And obviously, we leave promos as a strict W/L, since you neither gain nor lose LP from them. If someone wants to troll in their promos cause it doesn't lose them any LP, they're still not advancing, and though this can arguably be used by boosters to mitigate their buddy's LP loss, they're still losing LP, and anyone who has the lack of intelligence to say "oh yeah, I'm boosting and need to stay in x elo until my buddy can get to y elo" can "catch these bans" from Riot.