Ehhh... I can't help but feel like you're putting too much thought into this. As you pointed out yourself, the justification for making Raichu a psychic-type wasn't the most thought out piece of reasoning (the Dragon-type Exeggutor, however, is apparently because of 'Dragon Trees' or whatever they're called). Personally, if they did go the alicorn route with Rapidash, I feel they'd have to make it Fire/Fairy, with the Levitate ability... way more unique typing there.
Oh, you must be new here. That's what I do.
So, I
can find reasons why they made raichu psychic. Just, not satisfying enough.
They obviously wanted it to levitate, using its tail as a surfboard; the tanned coloring, clear blue eyes, rounder shapes and laid back body language bring to mind a relaxed surfer type, which, this being hawaii, is very obviously what they were going for; I couldn't tell you precisely in what his type informs the design beyond "surfs levitating" until I see what actual psychic moves it has beyond practicing telekinesis on itself (possibly confusion and psychic, and you can leave stuff like hypnosis aside).
But it's very likely they have no actual explanation because they simply liked the concept, they wanted raichu to have something this generation and they couldn't come up with a plausible environmental reason for why raichus started to surf on their tails in alola, and above all, why they don't do it in the water. If they had made an electric/water surfer raichu, it would have been self-evident.
Are they clear reasons in the context of the pokemon world? not at all. Are they clear in the context of our world? yes.
It's better when it's both, but we'll have to take it. You could say of any pokemon "they did whatever they liked" and not think it further, but then you'd be missing part of the message.
Well, seeing that alicorn is a creature of myth, and Rapidash is a unicorn to begin with, giving it a fairy type doesn't seem that far-fetched to me.
Oh, but in what does "being a unicorn" inform rapidash's design or characteristics? it was only later that its horn was acknowledged, and that was by giving it poison jab and megahorn, which aren't very magical attacks at all.
As I said, it's a very concrete, down-to-earth pokemon; that doesn't mean they can't, or won't, go the eighties' My Little Pony route with it (after all, they did eschew the electric/water surfer raichu if favor of a more esoteric typing), but it does imply a greater effort to mesh it with the old design (or to just leave it unexplained, which I doubt they will do again because the pikachu line is special), at least by what the known alola forms have shown about the rationale used to make them.
