Sure, that's fine. As long as we apply that in both directions.
You got an S but still lost? You lose extra LP for focusing on score and not winning.
Alternatively, we keep it like it is: 20 lp on a win, 20 lp on a loss, modified only by MMR compared to your rank, and average team MMR. Because League isn't about score.
Your S means literally nothing for victory or defeat.
The Nexus is the only objective that actually matters in the end. If you take every last turret and inhibitor, every last drake and dragon and crab, get herald and every last red and blue buff in the game, and grab baron 20 times, if you drop a billion wards and use a hundred thousand gold worth of control wards, if your team has so many kills the numbers run off the screen...It means literally nothing if they take the nexus first. Because you had all that advantage and you still lost the game.