The problem is that people would stop playing optimally to win, and would start playing to protect their KDA.
If I'm sitting at 7/2/1 and the total score is 10-15, that game is still winnable. Let's say it's a 33% win 67% lose situation here. Let's also say that with my current KDA in your system I'll lose 5LP, but if I keep playing hard I'll get -20LP or +20LP.
So expected values say if I stop I'm guaranteed -5LP. If I keep playing I net out at -20*.67 + 20*.33 = -6.67LP. I'm better off not trying to win, even though that game is winnable. This can be expanded endlessly, basically as soon as you think your teammates aren't good enough you'll stop caring about winning and start caring about maximizing your KDA to limit your losses.
There is ONLY ONE method of reduced LP gains/losses that I think stands ANY chance at being a reasonably fair implementation:
If the losing team has destroyed an inhibitor, the game is considered a "close game" and LP rewards are smaller.
Why?
Because inhibitors are a REQUIRED objective. At least one inhibitor must be destroyed in order to win the game. So fighting to get that inhibitor is completely in line with fighting to win the game. It's also often worth 2+ deaths to secure an inhibitor, as 5 minutes of increased pressure is worth more than 1min per death of lost pressure. It also is often a good indicator of a close game - I can't remember ever seeing a stomp where the losing team took an inhibitor.
Of course, we have balance issues then. Champions would need to be balanced not only around winning/losing strength, but also their ability to take inhibitors when behind. E.g. A Tryndamere with a 50% win rate would climb very steadily because he'd be able to just sacrifice himself using ultimate for turrets in a side line until he gets an inhibitor in any game he thinks he'll lose. Tryndamere's play this way anyways (so again, it's not a thing that takes away from trying to win, this strategy is still his best bet at winning) but it means this champion actually would benefit a lot more from this system than others. Likewise, a strong defensive champions that can defend inhibitors really well (e.g. Ziggs or Anivia) would likely be able to make sure all of their wins were full wins and not close ones. So I don't think this option would work either as it'd be too hard to balance, but at least it'd be consistent with the overall goal of the game.
Which is, remember, to win. Nothing else matters. If we're on the same team and at the end of the game you're 25-2-1 and I'm 2-25-1, but you didn't touch a turret all game and I single-handedly took down a full lane of outer, inner, inhibitor turret, inhibitor, nexus towers, and nexus, I JUST CARRIED YOU. Not the other way around. All that matters is the Victory screen at the end of the game. Kills may help you get there, but they aren't even necessary.
KDA : 1 11 6 (TOP)
KDA : 7 4 7 (MID)
