So we do know that the horizontal speed of the character in Smash is dependent on how fast you move the analog stick. But I do wonder if it is possible recreating this with a keyboard.

Nope, a keyboard is basically binary input - you're either pressing the key or you aren't. There's no additional information being made available beyond that. Not to mention that the sheer variety of keyboards that exist on devices would make this an impossible task as well; some keyboards have keys that actuate after you press down on them for 2mm (i.e. key travel of 2mm). Others are 1.5, 3 or any other value.

Some keyboards like the Wooting 2 HE have additional functionality that in theory could be used to do what you're talking about, but that would probably require modifying the keyboard drivers or otherwise getting that information from the keyboard. And it wouldn't be very portable either since it'd only work for that specific keyboard. All in all, you're better off just looking at alternative control schemes (like how fast you can double-tap a key) rather than try to do the equivalent of pushing a square block into a round hole.

It's part of why simulation enthusiasts prefer a wheel or yoke for driving and flight sims respectively, because they can provide several additional inputs that a keyboard can't fully emulate. It's not just because it's physically closer to the real thing.

I see, it’s true that a binary input can’t do much. It is preferable finding alternative control schemes like you said.

Thanks for the reply!!

Usually PC platform fighters either use a run key (for example shift + A to run right) or double tap to run.

Some do use these type of controls indeed, like Brawlhalla for example (even tho it’s technically a dash button)

Well you might be able to set up the controlls so that you have multiple walking buttons. One key that registers the stick fully going to the side, for a dash, one key for the middle position to walk normally, and one so it slightly moves verry slowly.

I think you can do something like that in some settings with Dolphin, if you're playing Melee or Brawl on a keyboard. I'm not 100% sure if you can set that up in Dolphin, but I do know you can do that for the trigger values, to input a speciffic value of the analog trigger being held in. So if you're playing Melee on a keyboard (or a PS1 arcade stick I tried it with) you can have one button for a small shield (trigger fully pressed) or a big light shield on another button, for an input that does the trigger ever so slightly pressed.

If it would be important to get more of an analog feel than you could get with suggestions like a Run key, an alternative might be to use mouse for movement. It would probably feel more natural to players for top-down than side-scrolling formats. And of course might not be an option if you're planning for 2 player local gameplay.

Never thought about using the mouse that does sound interesting.

So when you say multiple walking buttons, you mean multiple buttons that adjust the speed like an analog stick would?