I mean that's like, your opinion, man. Infinite was the best game out of the three for me. It also left the most lasting impression on me.
Agreed. Mechanically, Infinite is easily the best in the series. Best shooting, best traversal, best level design, most enemy variety. As a shooter, those things are pretty important and Bioshock has always been a shooter above all else. I also thought Infinite's story was a lot more interesting than the previous games. Rapture was a cool setting and had a cool backstory but it was pretty one-dimensional. Infinite's story is literally multidimensional. Its characters are much better developed too.
I think the biggest problem people had with Infinite was not with the game itself but with the fact that it didn't match their preconceptions of what it should have been. When people saw the initial E3 reveal, they imagined that Infinite would be an open-world shooter RPG where you jump between realities at will. When the final game wasn't that, they were disappointed. Expectations can be very dangerous which is why publishers and developers generally try to avoid revealing games until they've been finalized from a design standpoint. 2K made the mistake of revealing Infinite too early.
Meanwhile in Infinite, everything is literally stolen from the first game. Why are there plasmids in this world? The bad guy stole them from Rapture. Why is there an enemy that is a clear Big Daddy stand-in? The bad guy stole the idea from Rapture. Instead of feeling fleshed-out a lot of things feel completely nonsensical, the obvious example being the availability of powers in the market at the beginning of the game. Why haven't the powers had the same impact here that they had in Rapture? Why doesn't everyone take advantage of them? Infinite replaced a satisfying backstory with J. J. Abrams-style plot twists, which results in some cool set pieces but an overall experience that's far less memorable.
Eh... I really wouldn't cite the first Bioshock as an example of logical coherence. The notion of making super-powers readily available for anyone is absurd and one that Andrew Ryan would have never realistically allowed given that he was obsessed with holding power. Their presence in Infinite is actually more believable. Rapture was all about individualism and that, combined with super-powers, inevitably led to war and the city's downfall. Columbia, on the other hand, was all about the Prophet. Everyone in Columbia (except for the workers who didn't have access to Vigors) worshiped the Prophet and were united under his will. They had no reason to abuse their powers or fight over them because they all served the same master and had the same goals. Anyone who strayed from this doctrine was punished severely, as shown by the public humiliation/execution of the interracial couple.
As for Vigors and Songbird being literally inspired by Plasmids and Big Daddies, that is correct. This is still a Bioshock game after all and there are certain fundamental elements that need to be consistent between games. Super-powers and large, iconic enemies are one of them. That said, the analogy is a bit off. In Infinite, the Handymen are much closer equivalents to the Big Daddies, since there are multiple of them. Also, the Handymen are much more interesting to fight than the Big Daddies. Songbird was also way more awesome than any of the Big Daddies.