I think it is easiest to view this question from the balance and design approach of vanilla Melee, as that is the only thing we really have to go off of for a hypothetical Melee sequel, so fast-fallers and aggressive characters like Fox would be generally where they are currently in the meta in this scenario. And I think aggressive and fast play is one of the defining characteristics of Melee. Things would drastically change, however, if say... floaties were the predominant force in the top tier of the game.
Under these conditions, I think it would be unwise to assume that removing L-canceling, and having reduced landing lag would make the game strictly better. Here is my reasoning for that.
It would be impossible to deny that having a higher physical requirement for a character makes it harder to play. The more buttons you have to press, the more time you need to put into practicing tech and developing muscle memory. All other things being equal, the character that requires more inputs is more difficult.
Most tech related to L-canceling (SHFFLing and shield pressure) as many people have pointed out, are not terribly difficult once enough practice has been put in. But in the context of tournaments especially, there can be tons of variables that influence how consistent you are. Of course, the practice required to reach this level is a very real and daunting part of learning to play Melee at a competitive level. I personally believe this to be a good thing, but more on that later.
Fox and Falco, being the most physically demanding characters in Melee, are already a dominant force in tournaments, and will be for the foreseeable future. Compared to Marth, or say Peach, how many aerials are you L-canceling per match as a spacie? Every character that needs to L-cancel their aerials (i.e. all of them except G&W, wah-wah) is going to benefit from automatic L-canceling, but how much more so would spacie players benefit by not having that extra physical demand? In one set, or two, this may not make a huge difference, but I feel it would be short-sighted to not consider the long-term consequences of removing L-canceling. The longer a tournament goes on, and the more matches you have to play, the more the game takes a physical tole on the player. and I don't think this is bad. Yes, in a vacuum, people generally do not mess up their L-canceling, but it doesn't mean that L-canceling takes no skill. Every L-cancel is a bit of energy taken from you as a player and diverted to that action. And as we have certainly seen from this weekend's Smash Summit, one mistake can cost you a stock or even a game.
Just like with everything in Melee, you make choices and sacrifices when deciding what character to play and how to play them. What do you value more as a Marth player, neutral game or punishes? What do you value more as a Fox player, style or optimization? All of the decisions you make on how you develop as a player reflect what's important to you, and how you are going to handle interactions with other types of players. And I believe deciding how much of a physical requirement you want in the character that you play is a very relevant thing. In the top 8 of the tier list alone there is a wide spectrum of technical requirement. Fox is already almost universally considered the best character in the game. Now compare Fox's physical requirement to Sheik's. How much do you think the Fox player will benefit from automatic L-canceling compared to the Sheik player, assuming equal skill level? I personally wouldn't want to live in a universe where shield pressure required 1/2 the normal amount of button presses. Even if the shield pressure is almost always executed correctly, the more matches the Fox player has to play, the more difficult his task.
Ultimately, it comes down to how you view Melee, and Smash in general, compared to Esports. If you are a casual player, just hanging out and playing Melee with your friends, no aspirations to play at tournaments or to develop on a truly competitive level, then L-canceling probably matters very little to you. But the competitive scene is a bit of a different scenario.
Esports are literally electronic sports. That seems obvious, but it often is taken for granted. The main goal of the Esports movement, it seems to me, is to get the players of the various games (SC, DotA, Melee, CS:GO etc) to be taken seriously as athletes, which they most certainly are. Chess is not an Esport. I mean... obviously, but even if it was played on computers it wouldn't be. It's a purely mental game. It is certainly no less competitive for this, of course, but the very nature of electronic sports implies a physical component. And I think preserving this technical aspect of Melee, and Esports as a whole, is what separates these games from the wider array of competitive gaming, be it on a board or a computer.
Every sport has it's demands that it places on its participants. Runners blow out their knees. Boxers get concussions, or broken noses. Football players get concussions, torn hamstrings, you name it. Basketball players... more bad knees and such. The only catch is these people make a lot of money doing what they do, so we generally don't even question it. And those people wouldn't be making the kind of money they do if the sports they played weren't difficult and demanding and often required incredible sacrifices for great accomplishment. So the real question is, how do we as a community view the future of Melee as an Esport? Leffen said recently in the HTC Rivals video, that Melee is one of the few games to have survived almost solely on its game mechanics. I do believe a part of this is due to how difficult the game is to play, both physically and mentally. It drives people to want to improve. As spectators we can see the demand it places on its top players, and what it takes to achieve greatness.
Difficulty of execution is a very important component of traditional sports, and of Esports by extension. Half of the Olympic games are purely physical tests, and no one bats an eye at this. Why can't Melee, at least partially, be about testing who hits buttons the quickest, and most consistently? If you happen to be on the other side of the fence, and want Smash to be mostly a mentally focused game, then I'm not sure if there is much of a discussion to be had. You want something different from this game than I want, and that's OK.
At the end of the day, every sport is a series of arbitrary rules designed to make completing some task unnecessarily difficult. We kick the black and white ball all the way down a huge field into a net that has a dude standing in front of it, and he tries to prevent that, and gets to catch the ball with his hands, but we don't, and also knocking people down, in very specific ways, is totally fine. Yes, this is a gross over exaggeration of soccer, and the rules all work together to create a cohesive experience, but only in the context of assuming that soccer is the experience we want. These rules probably don't seem very fun to you if you want to play Tennis.
I think in the context of Melee, or an essentially Melee-esque sequel, L-canceling is fine, as the most physically demanding characters to play are also theoretically the best. I can see the argument being made that from a video game design perspective, L-canceling is essentially arbitrary which does not depth, but I don't personally want Melee to just be a video game, and I think this context has a lot of impact on the discussion.
edit: I clarified some wording.
As a side note... I think an argument could be made for Melee actually being one of the competitive video games closest to a tradition sport experience. So much of how your character acts is dictated by how you play the game physically, and how you choose to interact with the controller. With Melee being primarily an analog game, there is tons of room for personality both in play-style and general movement choices. It might be interesting to see some sort of four-way graph type deal that analyses where different Esport games lie in regard to physical vs mental demand, with something like 100m dash and chess representing the two traditional extremes.
