My biggest complaints about these two movies: Far too many references to the prime universe.
I mean, I get that it's a parallel universe and a lot of things are going to be roughly the same, but the constant references to things like Harry Mudd, Section 31, tribbles, Christine Chapel, Carol Marcus, Scotty the Miracle Worker, Khan the villain, etc. It's all a little too much.
Supposedly they wanted to do a reboot so they could be unburdened by the rest of the ST universes (admittedly) restrictive continuity. So why do they keep going backward? At some point it stopped being cute.