I doubt they would reboot so soon. So let's keep the same crew. Make sure Kirk has grown up. Just forget about the Spock and Uhura fling. It's inappropriate anyway, because he's a senior officer. Kirk, Spock and Bones are now a team similar to their TOS counterparts.
Enterprise (Hopefully refitted to Look better than the current incarnation) has just escaped some disaster and arrives in a distant alien star system. Like the episode tomorrow is yesterday, the ship stops in the upper atmosphere of a planet with two factions in a tense cold war(Think 1962). One of the factions is on the threshold of warp drive. Enterprise is severely damaged. No warp(And get rid of the new warp phenomenon. No Dune Space folds) or sub space communication. A part of the ship breaks away and takes out a building of the faction without warp drive. This faction believes the other side attacked them. They retaliate even though the other side denies it raising the possibility for all out war.
Once in orbit, the undetected Enterprise's crew sees the effect they've had. But they need to recover some technology which survived impact on the building. So they beam down disguised as natives, but are captured as enemy spies and later rescued. This heightens the tensions further. The side without warp tech detects Enterprise and believes its a secret warship created by their enemies and launches a full scale attack. The other side responds. So how does Kirk and crew save the day.
What would be the point of that specific story?
As much as I loathe Abramstrek, the scripts, while being incoherent messes, do have a point. Abramstrek 1 was about getting the gang together with a minor in-universe justification for the reboot. Abramstrek 2 is about putting the gang and Kirk's command ability to the test, making them ready for the 5-year mission.
Stories like that in the quote are fine for a TV show where you have 26 episodes per season, one episode per week. But is the story you come up with really worth to fill those rare
2 hours every 4 years?