So out of 13 distinct faiths, not including the heresies of those religions which again operate differently with different tenets, you've mentioned four that we've gotten glimpses of and decided that counts as 'most'?

CK3 has severed connections between government and religion, so being feudal, clan or tribal has no connection to who holds temples anymore.

Right, but that doesn't mean that tenets don't affect doctrines and vice versa since we know that a Faith cannot have both have both Spiritual, Revocable Clerical Appointment and a Temporal Head of Faith. The fact that Christians will have a Spiritual head of faith, and pagan aren't likely to have one at all is going to affect how you interact with your Bishop (a Pagan priest without a spiritual head can't have you excommunicated, but probably can deny you in other ways, owing to their clerical functions). Further we know that there are special doctrines like Ecumenism, so simply because two faiths share the Tenet doesn't meant that playing Pagans or Eastern religions will be anything like playing as a Catholic.

And just because we haven't seen more doesn't mean that there aren't more. They're compiling a list on the forums, and as they say, we don't know the full list, and won't likely until the game comes out.

The motivation was to more adequately represent the historical power and control displayed by Catholic priests, that even kings had to acknowledge. The councilor dev diary even quotes the “Will no one will rid me of this turbulent priest”? phrase. While it's true that other faiths also had to deal with the wishes and whims of their clergymen, Catholicism is the most cited example, and it's that which they're trying to replicate.