You forgot the part where Aya's damage doesn't completely suck shit
That's what I was going to say. Aya CAN actually do fairly respectable DPS, as an added bonus she has wind nukes, which as is already stated, are a little bit uncommon. She's also one of the best trash owners in the game with her speed. Fast like chen, and capable of aoeing. Her mass aoe wind nuke is often capable of ohkoing all those really fast pesky enemies like spiral divers, eyes of twilight, strategists, etc. Plus her moves are physical, not mnd-based. As people mention, there are less physical attckers than magic, so that always helps.
I honestly think people who prefer Sakuya just kind of make half-assed assumptions that group buff > single buff no matter what. But the fact is aya's buff is noticeably better, with much less delay, I think it more than makes up for that.
Of course, Aya isn't as tanky as sakuya, but she CAN take a hit from just about anybody, even if you gear her up for offense. If you just want a speed buffer, by all means focus on defense gear, in which case she DEFINATELY can take any hit.
They both hit abut the same for me, except Soul Sculpture's multi-target.
I found that Killing doll would hit for 0-> less than HALF of my standard-powered nukes (marisa's magic missle, chen's individual flights, etc)...with 0 being fairly common. Soul sculpture hits for a decent amount yes, but the delay is awful for bosses, and it really isn't any better than decent.