Further thoughts:
1. The goal shouldn't be "balance" but rather "incomparable advantages." If one Civ has an advantage to Faith Generation and can buy things with it that others cannot (like Indonesia or Ethiopia) then that's not really comparable to a Civ having extra production for 10 turns when declared war upon (like Australia.) You probably have opinions about which one is stronger, but since they're apples-to-oranges comparisons, especially as a player devises strategies around them and those strategies and exploits snowball around a randomly-generated map, making them "balanced" is a fool's errand. Especially due to the fact that:
2. Optimized victory strategies throw the whole discussion out of whack. If early domination is the clearest path to victory (as it is with Civ6) then new designs will fall into whether they can make a go at that or not, which is unhealthy for game design. A good number of players will still enjoy the game if it's purely about annihilating each other before the Medieval age comes around, but that's definitely not everyone, even if that's the most competitive, high-level way to go about things. Oh, right!
3. Different players want different things. Not just in terms of playstyle (though that's probably the biggest issue here. If I like faith-based culture civs and you like fast early-domination civs, what would balancing that even mean? Neutering your early units? Boosting my faith and culture? Giving non-dom-focused civs better early defense? None seem like great options, honestly) but also with where the fun comes from. Some play MP, others SP. Within SP players, some will want to take an undeniably strong civ like Gran Colombia and see how hard and fast they can run over a map on Deity. Others may play lower difficulties but with niche civs like Khmer to try to make them shine. Some might wanna try perverse set-ups like Mongolia on Archipelago or Phoenicia on Highlands just for the weirdness of it. The deeper we get into this, the less "balance" has a real meaning, in my opinion.
4. Balance, if attainable, probably makes things worse. There are numerical functions underlying all of the mechanics in this game and, yes, those of us who don't just play the game but hang out on these forums are likely to know them pretty well by now (or by rote, in some cases.) But still, if we aim for actual balance, that means trying to figure out the exchange rate of GPT vs Production vs. Faith and on and on, which is pretty unreasonable (and, again, going to be dependent on optimized strategies that aren't everyone's cup of tea) but even if that's possible, it reduces the game to numbers with different color paint on them. I'm sure that would be immensely satisfying for some players (I remember from playing Netrunner the degree to which the community would attempt to do this in order to value different cards, and I know it happens exponentially more in MtG) but it really takes the appeal away from it, for me. Alternatively, of course, we could make an objective Tier Ranking based on win-stats data, and try to play with levers from that, but that also skews highly towards certain playstyles and just reinforces (or negates, depending) the optimized strategies.
5. All that said, of course some balance is worth striving for. Spain is a civ I never look twice at because I just can't see the point of it when other options are available, for instance. And that's sad, but there, the gap is one more of interest and excitement than raw power. Because honestly, with this game, a skilled player could win against the AI with a purely vanilla, no-bonuses-at-all civ. If I'm avoiding Spain, it's not because I can't win a game with them, but because it's not worth my time to bother. So interesting design ideas will always be far more important to me than whatever "balance" means in this conversation.