I have to agree with all of your points here. But, at the same time, on the scale set by the other TOS reboot films, this one is the closest to Star Trek — in the sense that it has an interesting and complex plot, ensemble cast drama, & elements of the utopian subtext that characterized TOS. The other two have leaned much closer to generic-sci-fi-action — though Star Trek movies have always been a lot more action-oriented and a lot less talky than the shows.
Was the jokeyness a bit out of character for a Trek film? Sure, particularly for the reboot franchise; on the other hand, the other films in this group have been particularly over-serious grimdark fare (even as they used absurd plotlines that made “Spock’s Brain” and “Move Along Home” look normal), and so expanding upon the only redeeming quality of previous scripts — one-off jokes — is justified. (This is hardly out of line for Trek films; after all, the best — or at least most interesting — Trek film is The Journey Home, which is also the silliest.)
I more or less agree with MovieBob’s review here: Star Trek Beyond is, as a sci-fi action film, passable; as a Trek film it’s mediocre; as a Trek film in the reboot franchise, it’s surprisingly good, and would have been indicative of a worthwhile series had it been the first film. Because it’s the third, and because we’ve already lost some of the cast, the reboots as a whole probably won’t be able to recover, because even if the general improvement in quality continues, it doesn’t have enough remaining installments to become worthwhile as a whole.