The issue for me is more that Kirk's command decisions in the first movie are pretty terrible. Spock does all the hard work and Kirk skates by on charm.
Not that Spock's decisions were much better. Limping the Enterprise to the fleet at low warp is a terrible, terrible idea, just not as terrible as going after Nero.
Wasting an escape pod, which you may need considering the upcoming fight instead of beaming him to the brig on the planet. Terrible.
The right idea is to WARN people. You warn the Earth that their defence codes are compromised. You warn the fleet and tell them to get back here fast. If your comms are down, you fly to the nearest relay. If the fleet is out of comms range, or on silent manoeuvres, you communicate with the nearest outpost and THEY fly to the fleet, saving days if not weeks.
Beaming a single crewman onto the enemy ship. Terrible idea. Beaming two crewmen onto the enemy ship. Less terrible but still terrible.
Not exciting enough? Well, that really depends on how you tell the story. Neither Kirk nor Spock deserved promotion. Bravery awards or commendations, certainly, but neither of them showed particularly good leadership qualities.
And Kirk's leadership qualities didn't really shine in the second movie either, even if he is starting to mature. Troi failed her command test by doing exactly what Kirk did. Kirk is as good a command officer as Troi. Yikes.
If Kirk and Spock hadn't beamed aboard the enemy ship then there wouldn't have been anyone around to give out bravery awards or captaincies. Everyone on Earth would have been dead.
But I agree Kirk's captaincy has a lot to do with nepotism and luck:
McCoy basically smuggled him aboard the Enterprise.Nepotism.
He overheard Uhura's conversation about the lightening storm in space while hiding under a bedL. Luck.
Pike makes Kirk first officer.Nepotism.
Kirk meets old Spock who tells him how to defeat new Spock.Nepotism.
Nero does not destroy the Enterprise because he has another Spock to punish.Luck
Everything he did after getting on Nero's ship though has to do with Kirk's skills as a Starfleet Officer and future Captain.