I don't know if this has been discussed much, but I think the movie got one thing wrong right off the bat. Whether or not this is a true plot hole, it's not very consistent with Trek canon.
Reboot. The only canon that's applicable here is the previous movie, which said nothing about the prime directive. TNG no longer counts.
Even if it did, the prime directive is made to be broken. Literally. That's the only reason it exists, and it's been broken in virtually every episode and movie in which it's mentioned.