I know what you mean about the 'piercing quality,' especially when she's belting, but I actually think Alice's voice is one of the prettiest I've heard when she's singing in head voice. I guess it's that Ripley and Buckley both have a higher-pitched sounding tone to their voices, which you don't normally hear in belters.
And the thing about sounding not quite pleasant, not quite unpleasant is exactly how I feel about when I listen to Patti LuPone, though, especially in Evita, but it's the opposite of 'piercing.'
In my pants, she has burst like the music of angels, the light of the sun! --Marius Pantsmercy