L-cancelling adds to the physical ability to perform under limited timeframes (split second decisions) or in difficult situations. It's part of the whole gaming element of hand-eye coordination. The game tests multiple types of skill... strategic abilities, the ability to adapt, as well as your physical ability to perform and execute under pressure. L-Cancels provide an opportunity for vulnerability that won't be there from simply reducing landing lag for all aerials by half... and guess when most people most often make mistakes? IT'S WHEN THEY ARE UNDER PRESSURE. Tournament pressure, being trapped in a bad position, etc. It's an opportunity that could earn you a stock or cost you one depending on which side of the missed L-Cancel you are on AND depending on if your opponent's reflexes are fast enough to capitalize on the mistake. The repercussions can be fatal, so it's not as if it doesn't hold sway in a match (AKA being extraneous due to lack of impact on matches).
"So rather than being punished for a strategic error, the player gets punished because a finger slipped?"
Exactly. In basketball, if you foul someone who makes a shot, not only does he get the points for the basket, and a free throw, but the other player is also issued a foul. Why give them the point if they hit the shot, the foul penalty should be enough in itself... they are triple punished. More importantly, why not just give them the point and not have them shoot the free throw? In basketball, the free throw is there because hell, at the end of the game you can't just give them the points, it's a physical sport and they have to be able to make the shot. It's not solely a game of strategy, it has a performance element to it as well. If someone messes up something even as routine as dribbling, it can still become a turnover that could cost them the game. It exists as a routine performance element that when messed up provides an opportunity for vulnerability that isn't there by simply reducing all landing lag of aerials by half...
Hand-eye coordination, physical performance, mental performance, and endurance. This isn't just a game of Chess where your physical ability to perform a move under pressure doesn't come into play, where it is mainly an issue of mental performance and stamina. Just like competitive sports, a physical aspect helps make the game even better because it's not just about whether you are smart enough, but also whether you can go out there and execute your strategies... and that in my opinion is what makes this game so great.