I am trying my second game of BWN going wide (hardly did that with GnK) with piety, mostly just to experiment, so your comment caught my attention.
What is the particular synergy to piety with going wide? I am still early game, and I woefully underestimated my potential to spread my religion, so my beliefs were poorly selected. (This game is one of the few times I skipped Tithe, and I am really regretting that now! But I guess I can pick it up as a reformation belief?) Does Civ5 have a religious victory per se? How does one spin piety into a cultural victory? I thought I was just playing my current game casually to experiment with the SP trees, but now that I am vested, I would like to win! (Immortal, small continents, Indonesia.)
I actually never use title, yes gold usually problem for wide empires but some other options are attractive.
1) With piety your every city produce 5? fault just from buildings. If you have enough cities you can skip fault pantheon for something else, I recommend go full happiness for wide empires.
2) You will fall behind in tech and it is a good thin. The longer you stay in feudal age the more you can do with your religion. I tend to intentionally stay there as long as possible. (research every feudal tech but steel, stopping steel at 1 turn to finish and them research reformation tech you need, usually printing press for more happiness.
After that together with your happiness form religion kicking in you start to breeze try reformation and catch to ai in industrial.
Happiness pantheon, happy founder, as many happy religious building as you can get, cheap missionaries for enchanted believe and Jesuit education for reformation. Take happy from temple/shrine if no happy religious available.
Happy from your religion give more benefits more cities you have.
For many relatively small cities building production buildings is a limiting factor. So, sci building with fault let you have critical infrastructure the turn you discover tech and let you build other thinks.
Cheaper missionaries you will need to convert your cities to your religion, because when you build 10 cities and higher level first your cities will get your neighbor religion. That will give you opportunity to build HIS religious buildings first and then convert to your religion.