Disclaimer: I am not early access. I just recently went back to Galciv3 to see if the patch made it more fun. It did, slightly. I have played the series ever since Galciv1 PC, and Sins.
I must comment to this:
i think that people really have more fun when they're able to pick how their civilization works instead of relying on luck to give them a small chance on actually getting the type of civilization they were going for that game in a timely manner
Actually, on Galciv3 I don't. The custom civ traits are not balanced, so far and away some custom traits are better than others (which particularly, in Galciv3, are +1 Move and Xenophobic). I am not incentivized to mix it up and play different styles of civs, because certain traits are just definitively better. So I wind up playing my one custom civ that lumps in all the best traits, and play that 90% of the time. I think I would like the luck feature. That is not to say that is the BEST solution, however. I don't know. One serious concern I have with luck is, all I would do is re-roll a lot.
Switch over to Civ6: I have logged three times the hours on Civ6 as I did Galciv3. What Firaxis did is, they just have a boatload of civilizations. Yes, their styles are very different, but you don't have a lot of "traits" which different civs share, per se. They have outliers, too (namely, Babylon), which have clearly superior traits as well. But for whatever reason I gravitate away from Babylon; not toward them. Precisely because they're OP. Firaxis did a good job of patching and making their less-interesting civs more interesting (namely, Georgia and Mapuche). On civ6 I felt I could freely choose less god-tier civilizations and dial down the difficulty correspondingly. But for whatever reason, on Galciv3 I play the Tealians (my custom civ) every time, and I lump in all the best traits.
I really appreciate all of Brad's journals, blogging the game dev cycle, but I also appreciate all the rest of the devs and architects at the studio, who are also smart.