First off, just noting its senseless nitpicking bringing up that its not AP; I think everyone knew what the others meant. That said, yes, FF9 required the cost when the item was equipped.
Also, regarding Kyrie...
No, it can hit NonUndead, actually. BoF3 and BoF4 just have Holy resistance work weirdly, cause it effects Healing as well as Holy damage.
Typically, default Elemental resistance is 2, which is 100% damage, status rates are untouched, etc. Its equivalent to being neutral.
In Holy's case? Its 5. If you have less than 5, you heal less. At a 1 in Holy, you heal nothing IIRC. Kyrie works based on this value; at 5, you cannot be hit with it. If you have 4, you CAN be hit with it, but the rate is atrocious, and so on and so forth.
Thing is, so very little actually has below a 5 in Holy, and isn't undead. BoF4 did have an enemy, however that would lower your Holy Resistance, and then cast Kyrie on you I believe, and you wouldn't be "undead".
So yeah, Kyrie is actually Instant Death that is effected by Holy Resistance. It has 100% failure if the person is at least Neutral, but gets linearly better as they lose resistance, and has a brutal rate against Undead (who effectively are just 2x Weak vs Holy anyway, just Holy Weakness doubles as "Healing hurts you")
BoF5's Kyrie works probably the same way, since it seems to run off a very similar system as BoF3/4, just there's no Healing Spells or Holy damage, so its the only way it works.
Note that BoF1 Zom series and BoF2 Angel do EXPLICITLY hit Undead enemies, cause enemies have actual species in that game classified as "Undead"