I'll partially agree on the useless part, but why wasn't she supposed to be weak-hearted? Never once has it been said that PoHs in general let alone Kairi in particular was supposed to be strong of Heart. Ever.
Oh, I see your point. :3
But PoHs being a special existance, and also carrying the power to open the Door to Darkness make them have a really important role. It doesn't seems like someone with a weak heart could be qualified to be a PoH. At least not for me.
I could be wrong, though. ^-^'