I liked Rapture and the associated time period 10x more lol. Infinite was a good game, but just the atmosphere and story didn't do it for me like the other games.
Andrew Ryan was an amazing character.
Let me clarify this, I prefer Rapture myself. I have since a child loved underwater sea labs and cities (even to the point when I was a kid I would write down it as my dream home when asked the question on those kind of early childhood questionnaires), so obviously something like Rapture is going to be right up my alley. Mix that with the underwater city being set with 1950s aesthetics and themes, plus a crumbling society that's twisted and mutated, and you have an absolutely fascinating world.
But I still think Infinite has a charm to it that's different and engaging from the other BioShock's. Of course, the setting now is a very bright sky city full of 1910s stylizings, and in a city that's currently thriving rather than slowly dying, But the steampunk flair matched with the flashy 'show floor' (making attractive showpieces out of the boom of growing technology and enthusiasm for the show and arts, ranging from 'World of Wonder' attractions, extravagant mansions, old-styled diners, propaganda museums, and more), with a very attractive color schematic and many people to listen in on, objects to interact with, gift shops with hidden underground market departments to find, among many other things, I found to be a blast.
My argument isn't that I think BioShock Infinite is the better game, I think people completely blow its problems out of the water (pun intended) and will treat the game like all its composed of is its problems. I think part of that may just be people being bitter at it for some reason, maybe because they weren't as enthralled by it as BioShock, but I don't think Infinite is some bad game, and found it to be a very engaging world to be explored.
The world is completely neutered though, which makes it seem unrealistic and ruins the story they're trying to tell. The way Elizebeth is characterized alone basically disqualifies the game from having a great narrative of great writing.
While I don't want to get into the story too heavily for those who haven't played it, I don't think Infinite (or the original BioShock, for that matter) had anything remote to a realistic world, they're set in fantasy worlds that reflect and retract off real time eras, but in an exaggerated form with a fantastical twist. Outside of that, I disagree with your other points. The story I think fits the tone of the world, and visa versa (that's subjective, but I find myself in disagreement), and Elizabeth is a sheltered 'Disney princess' type in my eyes. I was okay with her, though she wasn't my favorite character of the lot, though know my sister took a huge liking to her when she played the game (she actually played it ahead of me and was curious what I thought of Elizabeth specifically, who I thought was fine and her arc and ultimate story purpose interesting), but I understand that some may dislike her... Bubbliness.
To respond to your edit, I like how they don't back down from the extravagant. The plot goes all in to some ridiculous themes, but manages to tie them nicely to their world, and I found an enjoyable ride with a satisfying conclusion, but that's just me. Trying not to say too much, but I enjoy some stories with elements that deal with the sometimes cooky, which might explain my love of things like Twin Peaks or X-Files. Not an apt comparison, but those manage to have larger-than-life elements and dumb 'silly' story things, but be entertaining and weave them nicely into their worlds and characters, is why the comparison came to mind I think.