Arceus-Fairy's prominence as a utility Pokemon perhaps has more to do with the Ubers tier than it does the Pokemon itself. First thing I'll establish is that Arceus-Fairy has access to nothing that other Arceus formes don't (except Fairy-type Judgement), so it's not an issue of movepool. It's entirely in the typing.
The Ubers tier is littered with Pokemon that have problems against the Fairy type. Very popular Pokemon in Ubers like Marshadow, Yveltal, Mega Salamence, Zygarde-C, Giratina-O and more are all walled or knocked out by Arceus-Fairy. It needs little more elaboration: it's just an extremely convenient way to check a wide array of threats. Couple that with Arceus's excellent movepool including Stealth Rock, Judgement, Defog, Recover and Toxic, and you have one of the meta's most prominent defensive Pokemon.
However, it's necessary to point out that it's not very helpful to say Arceus-Fairy is the best support Pokemon. First of all, if you count Primal Groudon as support, then there's really no competition; Primal Groudon is, without dispute, the best Pokemon in Ubers. Even if you don't, you still have the Water and Ground variants of Arceus, as well as Smeargle, Zygarde, Giratina and Mega Sableye, to answer for. Which is best is very situational, and if you go by usage stats alone, Arceus-Ground is actually the most prominent.
If the landscape of the Ubers tier were to suddenly shift, perhaps Arceus-Fairy and all those Pokemon would fall off in popularity. Ultimately, the reason the Pokemon is so prominent is because of meta. Arceus-Fairy is not popular because Fairy is intrinsically better than the other types, or that Arceus-Fairy is a better-equipped support Pokemon than other Pokemon. Circumstantially, it's just a Pokemon better suited to the meta than others.
And yes, Judgement is STAB on all Arceus forms.