Once again, too much to reply to, but much that is interesting to read!
Yes, tech level also feels undervalued. And as was mentioned by someone earlier, hammer output should be accounted for too. Anyway, I have a plan to do a big revision on how power rating is computed, and to also do some diplomatic adjustments (I want to tweak different values and decay rates, and also to create a diplomatic penalty for converting foreign cities). Then I'll do a big test for strength gain like for my previous AI tweaks.
Technically, this already does exist with the "Show Demographics" threshold, but that is the initial rung and a very low bar to clear. I think implementing a secondary tier that requires a more serious investment in espionage would be quite interesting! It makes historical sense and would help mitigate ridiculous and senseless wars between not even remotely neighboring belligerents based solely on a power metric that doesn't factor things like distance into the equation, and tying this to espionage would indirectly tether it to things like distance, as the allocated amount is itself likely to be a function of things itself indirectly influenced by distance, such as relations modifiers. I have no idea how feasible that would be to implement, but if you can figure something workable out, that could be paradigm shifting potentially.
The pretty harmless amount still triggers some separatism. To me it looks as if after the Teutoburg forest battle, the surrounding region got a few % roman. Or if the Volga region became a few % german after Stalingrad.
Personally, I actually like this mechanic strongly. Even your cited examples are immersive and plausible to me, as we indeed remember those places for the great battles fought there to this day, but only to the small extent that the names are remembered (
"... from this day, to the ending of the world, but we in it shall be remembered" - and so they are over 600 years later), and a would-be conqueror would certainly harken back to such historical battles were their enemies outright conquered. I think of it as a "prestige from battle" mechanism that ties a cultural identity to the land it fought on, scaling with the magnitude of the engagement, with the sweetly added touch that it also mitigates some of the arbitrary function of the way that borders work in Civ IV's culture mechanic, as you mention later on in your post. The combat victors might not have ended up winning the war or even conquering the land, but they will be at least known of and remembered for a long time if major bloodshed occurred there at their behest. In sheer gameplay terms too, it can help cement usable borders in partial wars, and ensure that mature and well-developed cities respect their new masters enough to be profitable (especially since, as you may not have found out, the unhappiness from foreign culture remains in RI even if you wipe out the target civ entirely).
The culture really disappears even if it's given in a peace treaty? I guess I'm never going to give a single city away... Better lose it militarily.
I believe your culture actually gets
replaced with theirs! Abandon and retake with all of this investment in buildings sacrificed, try to defend and potentially lose but keep my (sometimes strong) cultural presence, or cede in peace and give both to the enemy while keeping my forces are all pretty costly decisions in my experience...
Before commenting on some minor things, I do also want to echo as well that I love the attention to detail in all of the modeling in the mod. (Not only the scope and breadth of it, but the artistic consistency, as it all looks cohesive and not dissonant when combined together.) Really, I don't think there's any game that can compete in the same league with the scale of this mod in endeavoring to artistically depict human history. The fact that it feels and plays satisfyingly as a pure strategy game underneath really puts RI in a league of its own!
Some quick thoughts from my recent China game (which unfortunately crashed because of the recently reported intercept freeze

... though I was in a solidly winning position, so I'll call it a win.

):
- The icon for the Chinese Chu XP-0 fighter is of a USAAF P-47, and even has the latter's insignia! The actual animated plane looks correct, but the icon (or "button" as I have seen it referred to elsewhere in this thread) should be replaced with something that isn't obviously American.
- The whole machine gun line seems to lack the Guerilla promotion line entirely. Is this intentional, and if so, is that for balance or historical reasons? They are the first of their upgrade path, and a massively influential introduction when they arrive, so I could completely see that being by design, but want to ensure that it is not an oversight. As it is now, their only "hard counter" in their era is the early tank, and making them invincible on hills (where tanks already have a penalty in forests) might upset that balance too much. I just am having trouble conceptualizing why they wouldn't be able to have this ability historically. Is it their relative immobility? I mean, firing downhill is a lot easier, though that itself is already reflected in the defensive bonus for being on a hill, but I don't see why a machine gun crew couldn't be specialized to operate there. Just wanted to bring some attention to that in case it was overlooked.
- The animation for the air superiority mission is the same as that for air striking with the fighter. Couldn't you substitute it for the default "dogfight" one used for bomber interception? (I know that it's not a dogfight if it's an interception, but it still reflects aerial combat rather than bombing the ground.)
- I noticed that the Kingdom of Jerusalem in the Crusades scenario has iron and horses without any active trades or connections to either improved resource. Was this given to them as a buff?