I agree with OP, I find liberty should be the standard, and would lower tradition a bit, an rise honor a lot to try to balance them. Piety should give some extra bonuses, some culture and happiness would be nice. Piety is generally underrated, the real power of piety is getting a very strong religion, or enabling a religion when otherwise you would not have chances. Religion is quite balanced in the way you don't feel pressed to make a religion in any game in order to have chances, but definitively gives you an edge and extreme customization to what to improve in your empire. There are still some always-weak beliefs out there, and they damage ceremonial burial too much, a middle ground 2 happiness from each 3 converted cities (giving happiness from the first and third in each multiple), would be more fitting.
The great ingeneer makes more sense in liberty. Ingeneer = production, even we all use them for wonder more than anything, but if something liberty has over others, is a production boost.
Free buildings for 4 cities seem too much, and is a great part of the reason tradition is so powerful, with a four city setup you can go any type of victory, stay tall or go wide later, etc. The other is that the policies have great placement on order, and every benefit can be fully profitable in time. To rip it off:
- The starter is arguably the best. 3 solid culture helps much more than one per city, there's a point in the game that the culture from starting branches in minuscule, but 3 culture on capital plus plus sixtine, hermitage, broadcast fits better even then. Then you have the extra border expansion, with will along with the 3 culture, bordering absurdeness. You save LOTS of gold not buying land. Way down the best starter, even all others are pretty solid, tradition gets here the upper hand.
- Early monuments for free means LOTS of turns saved in such a critical stage, has the felibility to use that later for opera houses or any culture building, making tradition a great branch to mix with piety or honor. Free monuments plus the previous border growth makes a great synergy. 4 saves GPT at any time is great with the gold debuff, specially on early stages.
- Oligarchy being the worst policy, is quite powerful, not only for the free garrisons but the 50% extra power with them makes every city a stronghold just with walls. Taking cities with oligarchy and garrison takes a lot of time, and you won't use melee ever in such cities.
- 15% production for wonders is great and in great position. If you go wonderspam, is usually ready by the time you start with it, if you decide so, but if not, is a permanent bonus through the game. The you have extra happiness per 10 citizens, that will kick on the middle game and again in late game, and much faster on the capital, mena a lot of happiness if its not for short use.
- +2 growth in capital,and 10% from Landed Elite, being science the most important thing on the game, and growth directly tied with science, and 95% chances you capital will bi the higher city anyways is pretty solid too.
- +1 gold and -1 happiness each two citizens will go to more as the game advances, synergize with the capital growth boost and the finisher, making it a pretty solid policiy.
- The finisher also borders absurdeness, 15% to EVERY city, and 4 free aqueducts is quite strong (with the 4 GPT that is always noticeable), and not only that you get ingeneers for faith purchases later, is just crazy.
I would not debuff tradition severely, but just a bit here and there. Limiting free buildings and growth to 3 cities would make more sense, 4 cities is in the middle of tall and wide, at least in standard. Oligarchy 50% bonus is too much, seriously. I would lower it to 25-30%, good enough, you have the belief to boost it further and the freedom tenet, witch are way inferior risht now BTW. Lastly move the border growth out of starting branch, so you don't benefit for it so early and is not so massive, also would keep people out getting just the tradition starter because is so damn good. Maybe on Landed elite or Oligarchy, not sure.
Faith Ingeneer would fit better to Liberty, so move it to the lib finisher, and I would give also a +1 science on the finishier, to mitigate science penalty per city just a bit. Maybe a 3-5% extra unhapiness from citizens cut, to fit the lower happiness overall in BNW. Now is damn hard to get 6 cities up an running in standard in a reasonable time so it starts to kick on the middle game, and for standard 5-6 cities with liberty are key, if not just go tradition (I 95% pick tradition in Immortal/Deity just because of that and the free buildings to 4 cities, and I like more a wide style).
With Piety, +1 culture from shrines and temples would make you go through the branch faster, and maybe a +3 happiness once you get the great temple built to get some happiness boost. This way culture helps in wide style, and happiness only for a puntual boost, you have more flexibility on the religion benefits this way.
Honor need free units or early bonus production, to close the gap a little, free units to have an actual army, stack the garrison bonuses to walls intead, and some extra happiness from HE, strategic resources, forge/stables, anything that is tied to a militar way (not from all of those buildings, of course).
Consulates is overpowered with pledge to protect, I think lowering it from 20 to 15 should be enough. I wonder why firaxis ignore this abusable technique, if shouts for a change. I miss the faster decrease once you finish patronage, +1 gold from city states and moved great people as finisher... seriously??
Commerce is mostly fine, starter, purchase discounts plus science and the finisher are rather powerful, but the +2 gold from land routes and the 25% faster great merchants are a joke.
Exploration is nice but mixing culture needs (opener and finisher) with sea-based bonuses is horrible. The finisher should be a second policy so you don't have to plow on a situational tree just for extra artifacts.
Secularism is overpowered, I think all the other bonuses are right, the problem here is science by itself if too good. I would switch it with scientific revolution, or put sovereignty first, then revolution, last secularism. Only giving +1 science from specialists would work too.
Tenets I don't have a strong opinion on them, I find always a few very useful in each tree for designed victories, and are a clear upgrade on normal policies, I don't see a clear winner as you can tailor your victory goals with the tenets easily.
Lastly I would add some original policies tied to what the branches are for, and maybe some science boost in exploration, commerce has its pick on science and asthetics shouldn't, as science is oposed to culture.
Wow, I prolongued my monologue too far, sorry for the hard read.