Ah, one of those things never properly explained, but that most fanon agrees upon. Vaati's connection to wind. After all, there's not much in Minish Cap to suggest that he prefers wind over other elements, or even that he relies on elemental magic much at all. (Not helped by the fact that wind is represented with the colour green instead of purple in that one game, making it a weird exception to convention.) In fact, his attacks tend to be mostly fire and seemingly generic or lightning based balls of energy.

I think I've seen some authours and artists tackle it better than others. Particularly when it's used as part of his characterization. For my money, I've always been in the camp that elemental magic is a very intuitive form of sorcery, as opposed to more calculated and rigid rituals and incantations. Basically, if someone is magically inclined, they'll probably be drawn to one element more than others; an inherent affinity.

I also think it's decidedly apt for Vaati to have a profound affinity for wind. It fits his unfettered nature. It makes him a more interesting foil for Link, as they both have strong connections to the element. It even serves as a great counterpoint to other villains in the series, which are more commonly associated with fire, earth, or outright darkness.

All that said, Vaati went from being a tiny creature skittering across the earth that couldn't swim across a puddle or survive a fall from a single stair, to a sorcerer who lived in the clouds. His goals may never have been very grounded, but he proved the sky is the limit. (Do not hate me, it's involuntary. I have puns in my blood.)

I don't recall which game you're referencing with the color, I only really remember there being some tidbits in OoT about how the Forest medallion was intended to be a wind element, referenced both by the heavy wind themes in that section of Ganons tower and the emblem itself. I think forests are heavily associated with wind in Japanese culture, but I could be misremembering. Could be worse, it could be yellow as Air is traditionally represented (This is why I gave his teenage self a yellow robe under the hoodie, actually. I intended to draw a comic where he complains about it but haven't gotten around to it yet lol).

It's a natural thing to put him with considering he's expressly called a "wind mage" in FS. I do find it strange they didn't focus on that in MC but I just chock it up to different teams working on each game, and perhaps it not being menacing enough to draw pixelated special effects for. Rest assured he still loves him a good fireball too, though, I wouldn't deprive him of some flashy magic, heh.

Ah, sorry, I was a bit vague at times. When I say that Vaati's connection to the wind isn't properly explained, I mean how it is he came to be known as the Wind Mage and why he took up residence in the Palace of Winds. Since Minish Cap is a prequel, and Vaati starts off as an unknown enemy to Hyrule, one would reasonably assume it would become clear over the course of the story, but it just kinda... doesn't.

As for colour, I'm talking again about Minish Cap itself, but also the franchise as a whole in retrospect. Here, a quick reference:
https://zelda.fandom.com/wiki/Four_....._Four_Elements

I can't begin to count the number of times earth was green and air purple or yellow in other media. Because I just went to refresh myself and was thoroughly corrected. https://tvtropes.org/pmwiki/pmwiki......in/WindIsGreen

I swear, I was exposed to several evidently outlying examples of purple wind in my youth.

Huh, I had no idea the Earth element was purple. It's been 15+ years since I played it, lol. But yeah its right there in the tvtropes page that wind is associated with forests in Japan, so I'm glad I remembered that right, at least. I do like it as purple though, both because it looks good on him and because it gives it a sort of "dark wind" vibe that feels fitting (internally I've been referring to the staff I gave him as "Vaati's Blackwind Staff" which sounds suitably edgy, lmao)