A straight reboot would have had no emotional connection to TOS.
But to go for a straight origins story would have had two big problems:
1. Canon says that young Kirk was dour and serious as a cadet. That makes him overlap far too much with young Spock. There needs to be a contrast between the two main characters.
2. Seeing the characters as we know them develop could be interesting. But seeing both Kirk and Spock embark on different arcs, while still being essentially the same recognizable people, is far more exciting.
I think we're going to see more rage and dangerousness from Spock, and watch Kirk evolve into the familiar maturity and compassion but not start out there. In other words, as Kirk evolves towards TOS Kirk, Spock evolves away from TOS Spock, and what plotline emerges is anybody's guess.
After thinking about this (a lot), I'm convinced they took the best of the three paths open to them.
Well, not really. Previous time-travel adventures have all dealt with making sure that the time-line is preserved. This one just goes "fuck it".
My pet theory is that timelines can never be restored to exactly the original - that's like unscrambling an egg - so that every time Trek time-travelled, an alternate timeline was created, and we started following those
characters, leaving the originals in the dust, it's just that nobody noticed the difference before now.
And the only reason we noticed now is because the writers gave the characters weird, preternatural knowledge of the changed timeline - it still makes no sense that they could step outside their universe and understand "how timelines work."