the rest is rather garbage, but I doubt you've spent much time doing Culture VCs. Mathematically, Piety (vanilla) is a requirement for a culture VC. It's not just the free SP, but the boosts contained within the Piety tree that make it better for that VC.
I've done plenty of Culture VCs, and know how powerful it is for those wins. That doesn't make it well-designed. I think I was plenty clear that I knew that based on repeatedly saying that it was only good when you needed to get as many policies as possible (if it wasn't clear, apologies). And I never claimed it was just a free SP either, but that too many of the bonuses are just "it's easier to get other SPs." There's the opener (+15% construction speed on culture buildings = just more culture), Mandate of Heaven (just more culture), Reformation (GA is nice, but otherwise just more culture), Theocracy (baaaaaaaaad, IMO, and only does anything if you're building lots of culture buildings), Free Religion (just more culture, but at least it's also a free pick), and the finisher (just more culture, or rather, lower policy cost plus extra culture). The only three parts of the tree that do something other than make it easier to get policies down the line are Theocracy (again, baaaaaaaaad), Reformation (half of which is just about getting more culture anyways) and Organized Religion, which is actually pretty good.
IMO, it would be fine if the tree were good for culture-focused empires. It would even be fine, although probably still (but less) situational if the picks actually paid for themselves in culture over the course of the game which I'm almost certain they don't. I like sometimes playing, say, a war-oriented game in which I prioritize culture to get lots of good policies, instead of going just tech + hammers to get lots of good units. And if the tree were built with more policies like Organized Religion, which rewards you for getting lots of culture in a way that doesn't just make it easier to get another policy down the road, that would be terrific while still being good for cultue wins, as it should be. But making it so narrowly focused, with most of its policies built so nobody will get any benefit from over taking another set of policies unless their goal is literally to click on as many policy buttons as possible to win, shouldn't exist.
As for being necessary to a Culture win, well, yeah. It is. Which is another design flaw. In a game like Civ, there should be no instance of "you
NEED to take this specific route or you will
LOSE." Ever. For any type of win. Period. So it's worthless in most games, and completely necessary in the few others. Big. Problem. Hate to harp on this point, but 4x games are about letting the player make choices. When a choice like the Piety tree comes up, there's no choice. It's already been made. Are you going culture, take it, or (I haven't don't the math on this, but it sounds like other have) you will
never be able to win. If you're not going culture, then never take it because you'll always come out behind on actual actionable policies. Maybe dabble in it for Organized Religion if you can't get a happiness boost somewhere else, but most of the policies are literally the worst things you could possibly do with your culture.
Let me reiterate since it apparently got lost earlier on: that doesn't mean I think it's not a good tree. But it's either worthless or indispensable, which makes it poorly designed. Culture wins shouldn't need any one tree to be viable. Wonders like Hermitage or Cristo Redentor are one thing, since they're not taking the place of something else you could be doing unless you're desperately short on hammers. And you don't need to get every culture wonder out there to win culture, and more importantly, people playing for other types of wins can get some use out of some of the culture buildings because they're converting hammers into culture, not culture into less culture, which is the crux of the issue with Piety (again, unless you just need to hit that threshold of having clicked 30 different policies).
If those thoughts are "quite garbage," please feel free to point out how. But if your defense is just based based off of the fact that it's fine for a tree to be necessary for one victory condition and next-to-worthless for all others (again, aside from Organized Religion), I'd say that my point is very definitely not garbage. IMO, that kind of design diminishes a 4x game by removing the player choice element which is integral both to the core idea of the series (giving the player authority over how to run their empire) and replay value (by differentiating playthroughs even of the same type).
Final thought: I know it's likely that someone will say something like "Well for a science win you need libraries." Which is true. But it's also true that libraries 1) are good for all win conditions, 2) don't restrict the number of buildings you can build, unlike Social Policies, which consume a very scarce resource, and 3) most importantly, turn hammers into beakers, which is fundamentally different from, again
turning culture into less culture (which, again I will reiterate for the sake of clarity is good but only if you're trying to click 30 policies). All those things, and the last in particular, make other important-to-necessary techs/buildings/whatevers fine.
TL;DR: Nothing as scarce as SPs should be necessary for one win and garbage for all others; Piety would be better off giving bonuses for focusing on culture instead of turning culture into less culture (for example, more policies along the lines of Organized Religion or Theocracy).
) would be a hard one to make in most games/maps. I also hope that Piety remains a cultural SP or that another SP picks up their early boni. And perhaps I would add one more choose one or the other SP but not both.
and +3 
for Holy Sites and -20% faith cost for everything that's purchased with faith.
