1)That doesn't mean that the booker's that kept anna would be happy either, unless for some arbitrary reason none of the alternate universes had booker or anna being unhappy. In Universes A) Some booker and elizabeth's would be happy some wouldn't, B) Wouldn't some elizabeths and booker inevitably end up with an unhappy life too?
2) My issue is, Elizabeth's relationship was the best thing about the game for me. The quantum/time travel was well fairly well done, but not more so than a movie I would give 3.5 stars (Looper). It's obviously a preference. There was nothing wrong terribly wrong with the ending from a mechanical standpoint, and is really quite good for a videogame. Just imo, it abandoned the games strengths for an ending I've seen before though not frequently, that's my criticism.
To say I want a hollywood ending is idiotic, and non hollywood endings are really quite available to see.
Looper has an ending that's extremely similar to this, but was more emotionally satisfying and still had issues. 12 monkeys has an ending that's similar to this. Lust, Caution, Oldboy, Infernal Affairs, Pan's Labyrinth, Ghost In The shell, blade runner different story's with not typical endings that are my favorite movies. Stein's gate is visual novel game like thing, which has like 9 endings caused by various consequences of time traveling, specifying the rules much more clearly.
1) That's the thing about the multi universe thing, if a person is happy in one it doesn't mean the other is. There's probably millions of Bookers who are unhappy with Anna, but that's something we have to realize that will never change. But the point of the game is to stop the tortures and the kidnapping Comstock did to Elizabeth, that was the ultimate goal of the game. The other things are just questions that don't really have an answer.
2) I agree that the relation between Booker and Elizabeth is amazing, and it's sad to know that the relation will never happen in the future, but that's the best for the characters. The relation was great yes, but at the expense of a crazy man who kept her daughter locked and torture her, not "knowing" each other like that is probably a happier solution.
Never watch Looper but I agree with some of the examples you mentioned (especially Pan's Labyrinth), one game that also has a mindfucked ending is 999 for the DS (9 hours 9 persons 9 doors) it's also a visual novel, I recommend it if you haven't played it.