Chaosmancer
Legend
This does give an interesting notion to how the power hierarchy would go if you assume bishops did not have big spells.
Could a 5th level cleric just walk up to a Bishop and claim higher religious authority? (god gave me spells, I clearly speak for him more than you). I could certainly see players attempting that argument.
I think they absolutely could and it would logically follow, given the standard DnDisms. If you have active gods who actively give magical power to those blessed to enforce their will, then more magical power = more blessings/more important duties = more authority.
Now, there are a lot of ways to work with this, a lot of different world-building levers you can pull or shift, but there are two I find particularly interesting.
1) The most important positions of authority become wandering adventurer clerics. This is a shift in how we think of religious structures, but it could be the battered armor of a traveling cleric is seen as more of a badge of office than the silk robes of a church leader.
2) Since NPC abilities can trivially be different than PC abilities, PCs get the combat focused magic, and the NPC church leaders are instead blessed with powers suited for their role. Such as much more powerful and complex divination magic (allowing them to send adventurers on quests) or community wide magics that protect from various evils. Things that are more powerful, but that aren't suited for the types of combat a PC gets involved with.