In fact, his arguments against nonlocality were later disproven experimentally in the '80s, as quantum mechanics allowed for much higher fidelity predictions than could be explained by a hidden variable theory [0].
I don't think anyone _likes_ the Copenhagen interpretation per se, it's just the least objectionable choice (if you have to make one at all). Many-worlds sounds cool and all until you realize that it's essentially impossible to verify experimentally, and at that point you're discussing philosophy and what-if more than physics.
Intuition only gets you as far as the accuracy of your mental model. Is it intuitive that the volume enclosed by the unit hypersphere approaches zero [1] as its dimensions go to infinity? Or that photons have momentum, but no mass? Or you can draw higher-dimension Venn diagrams with sectors that have negative area? If these all make intuitive sense to you, I'm jealous that your intuition extends further than mine.
Copenhagen, on the other hand, doesn’t offer a workable model of how and when the wave function collapses, and doesn’t offer any predictions in that way (there are theories of wave function collapse that actually make predictions — some of which have already been falsified by experiment). For that reason Copenhagen isn’t “least objectionable”.