for everyone in the OP, but I like to accentuate these things.
As a long-time fan, having played the series since Civ1, I'll disagree. There was a time when I liked to have exact control over everything, but these days I want more randomness keeping me on my toes. I realize that's more along the role-playing playstyle for Civ and goes against the warmonger and builder playstyles, so it's the perfect sort of thing to include as a modular rule.
The wonder mechanic you're describing is just not what Civ is all about though. You're essentially wanting to really force certain wonders only for certain Civs. You sorta get that already in Civ5 with starting biases. No mountains? No MachuPichu, but Incas usually start near mountains so they have a better chance of grabbing it.
But ultimately, any Civ has a fair shot at building it. If they have mountains.
Whether you like it or not is sort of irrelevant. When I say 'civ players' I'm speaking of the community as a whole. Watching reactions by players to removal of control, perceived or real, has convinced me your suggestion is horrible and will not go down well.
That said, it may work as a sub-system, like collecting great works in BNW, but it won't work as a main draw. 'Come pick a Civ and have no control over what wonder you build' doesn't work well as a bullet point.
So again, you don't simply select "build great wall" in this system and have it done, but you can guide your civilization towards building the great wall, just as in Civ4, you'd guide your city towards building a Great Merchant or a Great Artist by doing the things necessary to increase the chances of that happening with the tools provided.
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I get that. But that's a whole lot of tweaking and cajoling to maybe get the wonder you want.
It can work as a subsystem though. Maybe a Civ with a lot of farms will get certain bonuses to build a wonder with a farming oriented flavour.
What I don't agree with is your flavouring of wonders to attach to only certain civilizations and all the hoops people have to jump through to maybe get a wonder they want. Too much work and too much uncertainty.
At best, you can have a system where you get a discount for certain wonders if you orient your civilization a certain way. Now that requires planning and strategy. Something people will want and enjoy. Wonders will have to be tagged with different labels, but it's doable and could work. But ultimately, China is still going to build those pyramids if the Chinese AI or human player decides to go for a pyramid building strategy, whatever that may be. And yes, they get to pick the Pyramids from the drop down and not just hope their Civilization pops a pyramid instead of something else.
Besides there are not enough wonders out there for each Civ to have their 1 wonder and also build others. Most Civs only have 1 wonder in Civ5, if at all.