Ah, yeah didn't play a lot of ToA. I seem to remember them having special techs. Turn 1 was like, you get a galactic achievement, you get a galactic achievement, everyone gets a galactic achievement.
Yeah, galactic wonders for each race as a way to specialize them was a little weird for that.
In all honesty, I like civilization-unique wonders much better than game-unique wonders. It differentiates the civilizations a bit, and (if done well) helps to emphasize the values of each civilization (e.g. the Altarians value culture and approval and their wonders reflect this, whereas the Thalan value efficiency and productivity and so their wonders are more focused in that direction, while the Drengin would get things emphasizing their more militant ethos). It also lacks the silliness of "oh darn, Pete built his Pyramids first; well, boys, I guess we'd better call it a day on this one, because we certainly can't finish our giant piles of rock now," or of "we have the technology to make this superb factory, but, well, George already has one and so we couldn't possibly build it despite it being far better than anything else we currently have, oh, and we're also at war with George and creating one would go a long ways towards evening out the fight."
Some things, e.g. the Temple of Artemis at Ephesus or the Great Pyramids of Giza, just aren't appropriate as wonders that anyone can build - these are things that only certain kinds of cultures would build; Buddhists aren't going to build a temple to a Greek goddess, though they might carve giant Buddhas into a cliff face. Other wonders, e.g. Leonardo's Workshop or Adam Smith's Trading Company, are more appropriate as things that one lucky person who fulfills the right conditions should get, rather than as things that just anyone can "build." There are a handful of things which might justifiably be unique per game, e.g. things that rely on their prestige for their effect (to some extent, the Great Library of Alexandria, though the success of that one was based in part upon being heavily sponsored for a long time by one of the richest and most powerful empires of the ancient Mediterranean world, rather than simply being the first "completed" great library, and that library isn't nearly as unique as might be thought even in the ancient Mediterranean world), or things which are highly expensive and/or part of a cooperative effort (many space programs, the Large Hadron Collider, the International Space Station, etc; it'd be kind of nice, really, if U.P. proposals could spawn game wonders, e.g. a U.P. Headquarters, or the research wonder coming from a U.P. collaboration project and giving full bonuses to the player who gets to build it and partial bonuses to everyone who's part of the U.P. Council).