The thing about making a moveset that could fit multiple different characters, is that you almost always either A) make it out of character for at least one of the characters involved, and/or B) you miss out on much of the unique potential of, and thus the reason to make a set for, at least one character. I'll illustrate my point with an example. Let's say you took Luigi's moveset, and put Mario in instead of Luigi. It'd be weird, right? Luigi's moveset, with its awkward movement, scaredy-cat animations, and overall strangeness, is handcrafted specifically for Luigi and what makes him unique. Mario has none of those traits. This is an example of a set that's made specifically for one character, which is a good thing; it conveys the character, and combines it seamlessly with the moveset. For another example, although of a different type of uniqueness -- props and abilities instead of a general, slightly subtler theme -- take Kirby's moveset and give it to Bowser. Or Villager's set to Little Mac. You get the gist.
Now consider Captain Falcon. While his moveset is rather awesome, it's not really tuned specifically for him; any regularly-shaped guy could use that moveset. (And no, the fire and such don't make it unique to him; he never did that in his games either.) This makes sense, considering Smash's early origins as a fighting game with regularly-shaped guys; this would appear to be the remnants of that early phase of development. Nevertheless, we can still use it as an example. It fits the character, but isn't unique to the character, which should be strived for. Smash doesn't have any actual instances of characters with out-of-character elements in their sets, but the stuff I mentioned earlier -- like Bowser with Kirby's moves -- is a good theoretical example of that.
But what does any of this have to do with Toad? I mean, they're pretty much the same person, right?
Well, no. Captain Toad =/= WW Toad (and it's reasonable to assume that Captain Toad =/= "The" Toad). But they do the same things, right?
No, actually. Captain Toad never did most of the WW stuff. He never had a fairy lift him up, he never ran up walls, etc. Similarly, WW Toad lacks a backpack, headlamp, never plucked turnips, didn't use the gamepad glove, et cetera. And neither of them rode karts, shot out spores, and did other things that "The" Toad did (and even then we run into the issue of not being unique, as other Mario characters have gone karting and such). There's the possibility that "The" Toad is also WW Toad, but I digress.
With a unified "Toad" moveset, we run into the issues I mentioned above. If we use unique traits from both, it's out of character -- WW Toad doesn't have a backpack, and Captain Toad doesn't use bombs, so giving them those traits would be out of character. If we only use traits shared by both, then it's in character, but not at all unique (and even if the two did have some semi-interesting traits shared between them, you'd still be missing out on the unique potential of both characters).
TL;DR: Making a "one size fits all" moveset either makes it out of character, since character A never used character B's stuff, or you miss out on the unique potential of both characters.
Now if you'll excuse me, I'm gonna go watch the new episode of Extra Credits.