Not every verse uses Supernatural Willpower as a source of abilities. D&D doesn't, shit's just a boost to their literal Willpower stat (resistances). In expanding it, you limit something that I don't feel needs limited in this way. So I still vote no.
Not every verse does, true, but some do, and then there's others where it's just an ability in itself but differs significantly from other verses' takes on it, and the types were made largely to address the latter, and also the former though to a lesser extent. There's so much variety in SW across fiction, and the types were added to more directly address that variability on the PnA page itself, which I believe to be proper.
Referring to DnD, your take is fair, but their presence on the page is due more to Tarrasque being able to say "lol nah" to probability and make a failed roll succeed just by willing it so, Empyreans being able to do the same to attacks that bypasses their resistances, and SR users such as Sertrous, Asmodeus, and others being able to just force Holy power to manifest through their sheer will and belief, no divine intervention required. And besides, depending on the resistance, Willpower could fall under SW. Irl, there's things you simply can't will yourself through, such as being inundated with a lethal poison. I am admittedly a newbie to DnD lore and mechanics as well as to the game itself, though, so if you were to tell me those abilities are at most only tangentially tied to their force of will and explain why, I probably won't fight you on it.
And I have no intent to limit SW. I want to further explain what it's shown to be capable of across fiction, which if anything is the opposite. The types aren't some be-all-end-all, they are a compilation of similar expressions of the ability, done so for the sake of brevity and to better codify an ability that is very often subject to the subjectivity of the authors that implement it into their works. That subjectivity is somewhat poorly tackled by the current page, which is one of the shortest and vaguest PnA pages on the wiki.