Here's my thoughts on Piety...
I don't think it needs to be a viable "pure" opening tree like Tradition and Liberty, but is fine being one that you dip into alongside some policies from another tree.
For me the problem is twofold: there's too much religious benefit without Piety, and there's not enough religious benefit from Piety. Piety primarily boosts Shrines and Temples, but these are a terrible way of generating faith since they're so ludicrously expensive. I would like to reduce the benefit of being a passive bystander or minor dabbler, and increase the benefit of really investing heavily. A big part of this is increasing the importance of shrines and temples as the primary sources of faith.
I would do the following:
Cut down external sources of faith. Still really important, but no longer the major source of faith. Those who invest heavily in shrines and temples will have a much better chance of founding a religion, so it's a bit less of a crapshoot.
Desert folklore: Only faith from non-floodplain desert (or even just +2 faith from oases)
Stone circles: +1 faith from quarries (and maybe +1 science)
One with Nature: +2 faith from natural wonders
Tears of the gods: +1 faith +1 gold from gems and pearls
Natural wonders: halve faith output (some of these are huge)
Stele: -1 faith
Monastery, Mosque, Pagoda: -1 faith
Religious city-state faith reduced
Piety tree:
Opener: Allows you to build shrines, temples and the Grand Temple in half the usual time
Some day I want to actually build the Grand Temple.
Organised Religion: +1 faith from all religious buildings (shrine, temple, stele, cathedral, pagoda, monastery, mosque)
Just weaken the faith building snowball for non-Piety civs and sweeten the deal for those who go Piety.
Theocracy: +1 gold from all religious buildings (shrine, temple, stele, cathedral, pagoda, monastery, mosque). +1 local happiness from Temples in cities with a majority religion. Available as a second choice.
I think this is more useful than +25% gold from temples because it offsets the ridiculous maintenance cost of the buildings in the early game when you're actually building them (and the benefit isn't only in your financial centres). And an extra golden sweetener to the faith buildings for those who go Piety. Happiness from temples kinda duplicates one of the follower beliefs, but I feel like religions need a little extra happy and this lets you expand a little more without being railroaded into choosing a happiness religion and/or desperately needing Monarchy or Meritocracy.
Mandate of Heaven: 25% discount on purchases with faith
Bump it up a little to compensate for the lower amounts of faith floating around.
Religious tolerance: Gives the second pantheon belief in cities with a majority religion. Double faith generation from religious city-states.
To boost religious city-states back up in faith generation. I think it's fine to have this outside Patronage since the Patronage player will be much better at actually being friends/allies with the religious citystates.
Reformation: Reformation belief if you found a religion. New cities start with the majority religion of the city where the settler was built.
A small sweetener for those who didn't found a religion, and captures the vibe of the religious colonisation during the Reformation period.
Finisher: Free Great Prophet. Holy Sites give +3 culture, +3 gold
Pretty much fine as-is, just moved the Holy Site gold here so Theocracy isn't too strong.