Great post. I feel mostly the same way, except I never bothered with JJ's 2nd movie because I was too disappointed by the 1st one.
The real problem with Star Trek, however, was that it was unrealistic in its optimism and with everyone having such excellent values. They said many times in the series that genetic engineering was bad, was banned, etc. (except for that 2nd-series Pulaski episode in TNG, for some odd reason), but the only way humanity is going to be that moral is if it's engineered into them, or we do something to engineer sociopathy out of our species. Right now, sociopaths are in charge, and are exceedingly common, and their values permeate our society. Just look at the replies to your post: these days, the only thing that matters is money and profit, that's what makes a person "good". Even the Christians will tell you this these days: God favors people who make more money, and loves rich people more, and poor people are poor because God has abandoned them. Popular TV preachers like Joel Osteen will happily tell you this, and countless Christian churches preach this theology.
Of course, even Star Trek had its dark side, but it was in the past: we were supposed to have the Eugenics Wars back in the 1990s, and we're supposed to have WWIII sometime soon. Only after all that calamity is Zephram Cochrane supposed to invent the warp engine, meet the Vulcans, and quickly propel us into the galactic neighborhood as seen in STE, with humanity going from a war-torn society to eradicating poverty inside a century. So according to ST, we're supposed to be living in a pretty shitty time right now. That seems ridiculously optimistic however (that going through WWIII and meeting the Vulcans will suddenly turn us into a wonderful race of moralistic do-gooders without a bunch of sociopaths running our society like we have now).
What I like to tell people in discussions like this is that Star Trek does show our society, but not in the normal episodes; they're in the "mirror" episodes! That's us: the evil humans who run around murdering and conquering anyone and anything we can. If we ever invent warp drive and phasers, the galaxy is going to wish they only had the Klingons to deal with.