I haven't seen this movie yet, but plan to.
I loved the old Star Trek, and the Next Generation. Voyager left me cold. But....
I'll duck because I know that what I am going to say next will get me flak:
The whole Star Trek premise, from its beginnings until now, was built on the idea a Socialist Utopia. Forget "one world government" -- this is "one universe government"!
The Federation is an intergalactic multi-world UN with military "teeth". No one in the Federation every talks about money, except the Ferengi and they are "greedy capitalists". No one comes from "a country", although main characters clearly had accents. Spock's "The needs of the many outweigh the needs of the few --or the one" is the antithesis of individual rights.
I've always been able to enjoy Star Trek purely as fantasy, because the life that they describe could never be -- it is a utopia. But I am not so sure that other people (especially kids) raised on it have been so unaffected.
Roddenberry definitely got into the "Brave New World" concept, and the "prime directive" of non-intervention was another premise of us leaving more primitive cultures alone. In the original 60s version, there were definitely UN implications to the Federation, but it actually played out that the Federation was more like NATO, with the Klingons being the Soviets and the Romulans being the Chinese. This simply scaled the earth to the galaxy.
Even in the original series, I believe Kirk made a reference to there not being money, but this seemed confined to the military/exploration part of the Federation, as they made ports of call and apparently bought alcohol there. I think they deliberately kept this part loose, as is common with TV series (how often did people pay for drinks in Cheers?)
TNG lost me because Patrick Stewart would surrender the Enterprise to a life boat. They had way too many stories where surrendering was the "right and noble" thing to do. One of the things I like about the Kirk character is that he doesn't believe in the no win scenario and in this movie neither he or his father would ever consider surrendering their ship.
Another thing that lost me with TNG was that they got completely away from true science fiction and became totally new age. I remember reading an interview where the writers were bragging about how for TNG they would write plots, but instead of coming up with a real scientific solution, they'd write "insert techno-speak here" and have somebody insert scientific gobbledy-gook, usually involving tachyon particles. There was no true scientific principle behind many of the "solutions" to problems in TNG.
The abandonment of speculative science fiction for new age dogma hurt the franchise badly. Worf was also the best character from TNG, but they kept writing his character down. He should have been the toughest guy on the ship, but Data, Yar and everybody else beat him up. The franchise further degraded when Deep Space 9 deleted the "hopeful future" that Roddenberry created, replacing it with losers stranded on an out of the way docking station. In Voyager, the only memorable characters were the holographic doctor and Seven of Nine. The other characters were weak and insipid, including the captain.
Nobody's going to want to reboot any of the other series. I have to agree with some of the other posters that there's a "Muppet Babies" quality to the movie, in that the characters are VERY young to be assuming the levels of responsibility they do. Yeah, there's a certain idiocy to having a suspended stowaway assume command of a starship (I could imagine if a guy left the brig of an aircraft carrier and showed up on the bridge, assuming command.) In TOS, however, there were 450 people on the ship, of which apparently only about seven had actual jobs. Whenever there was extreme danger on a planet, the captain, the first officer and the ships's medical director beamed to the surface, while everyone else ran back and forth in the corridors.
The original series had money...IIRC, in the trouble with tribbles, the tribbles were being sold, as was the alcohol. In fact, I think there was mention made of possible profit. Also mining for money, etc.