I'm not sure I really like this idea.
There are three types of differences between the various civs: cosmetic differences, AI differences, and actual functional differences. Cosmetic differences include different civ name, color, leaderhead, city names, great leader names, and the graphics for certain buildings. AI differences include things that only affect the AI's playing of a specific civ (like how agressive they are). In Civ 1 and Civ 2, cosmetic and AI differences were the only differences between civs. Civ 3 introduced some functional differences: unique units and civ traits.
While I admit that I do like the UUs and traits, and think they add a nice touch to the game, I also believe they opened up a dangerous can of worms, and I don't think the idea should be taken too much further. The advantage of functional differences between civs is that it makes playing one civ different from playing another, so that there can be more variety from one game to the next. The disadvantage is that they constrain you by encouraging you to play in certain ways with certain civs. For me, some of the fun of civ has always been that when I play a civ, I can make their history turn out very different from their actual, real-life history. But the more "unique" each civ is (i.e., the greater the functional differences between each civ) then the more each civ will be pressured to follow the same path of development in each game. In other words, I don't mind some minor differences between civs, because it makes it more interesting to try a new civ after you've had experience playing someone else, but I don't want to see major differences between civs, because then I'll have to pick a different civ if I want my game to turn out significantly differently. I think the characteristics of each civ should always have a smaller influence on the course of the game than other factors such as geography, resources, strategy, etc.
Having said all that, I'm not sure exactly how significant the differences Kiech is proposing are. It sounds like the proposal is for actual functional differences, not just cosmetics. Its hard to tell... the English and Japanese temples already look different (a purely cosmetic difference, to be sure). Ball courts vs. burial mounds - would these do the same thing, and just have different names/graphics (in which case the difference is cosmetic) or would they actually do different things, resulting in functional differences between civs? The suggestion that certain civs can research certain techs that others can't is certainly a suggestion for functional differences, but then I can't tell whether the proposal is that these differences be in the default game, or just the editor. Doesn't Conquests already have this sort of thing in the editor?
If the functional differences between different culture groups are minor, then I'm all for this idea, but I don't like the sound of differences in available techs (not for the default epic game, anyway... mods and scenarios are a different story). If the techs available are different, that strikes me as forcing certain civs to always be played the same way. You'd have to always follow the tech progression dictated by the rules; you wouldn't be free to pursue techs that your particular civ never pursued in real life. Civs shouldn't be forced to be too similar to their historical counterparts... Civilization is a game of alternate history.
One last thing to consider is playtesting. Currently there are 31 civs, and 7 different traits. That means the designers of Civ3/Conquests had to balance 31 different UUs and 28 different two-trait combos in order to make sure that no civ was inherently better or worse than the others (or at least, not noticeably so). Every further functional difference between civs complicates playtesting further by making it even harder to achieve balance between all the civs. If you let American civs like the Mayans and Incas research sacrificing, but the Meditteranean civs cannot, then not only do you need to make sure that sacrificing itself isn't unbalancing (i.e., that the Meditteranean civs have something else just as good) but also that it isn't unbalancing in combination with the other differences. What I mean is, perhaps sacrificing wouldn't be particularly great in general, but would be super-useful if you also happened to play an expansionist civ, or if you had a UU that could enslave, or something like that. Each time you introduce a single set of new differences between civs, you dramatically increase the number of possible permutations and combinations of differences, running the risk that some particular combo will be unbalancingly strong or weak. Only careful playtesting can uncover these imbalances, and there's only a finite amount of playtesting that can get done before a game is released.