For me it will always boil down to the fact that I didn't like any of the characters in Trek09, especially Kirk. Honestly, they let a cheating arrogant undergrad jerk have the Enterprise even though he back talks his superior officers in front of the whole crew, assaults on-duty officers and provokes officers into fights. And this idiot actually complains about how being left on a planet is a violation of Starfleet protocol. Hey, if you're going to talk about how Starfleet protocols should be taken seriously, you might want to set a better example a**hole.
You're right on most of these points except the fight bit, that was a deliberate act that was designed to provoke Spock and cause him to lose control over his emotions thus allowing him to take command. All of that was because old Spock told him to do that and that he needed to do that because only Jim Kirk in command of the Enterprise had what it took to save Earth, so it wasn't like he was just being insubordinate or rowdy.
My criticisms of JJ Trek are a bit more nitpicky like the design of Engineering. Holy crap that's one huge engineering section and it looks nothing like an engineering section of any modern sea going vessel or like any engineering that we've seen in previous incarnation of Trek. It looked just like the industrial manufacturing/processing plant that they apparently used as a set. It just showed a lack of imagination, in my opinion, instead of designing a proper engineering they just found some industrial plant with lots of pipes and conduits and called it a day.
The other problem I had with JJ's Trek was making Kirk the captain of the Enterprise at the end. That's just ridiculous, sure he save the Earth but he's still just a cadet who hasn't graduated and while he successfully commanded a starship in one engagement he would still have a lot to learn about being the captain of a starship. What's more, this rookie captain commands a ship that's manned almost entirely other cadets who also have not graduated from the Academy yet and, at best, have had no more than a cadet cruise worth of experience underneath their belts. Who, in their right mind, would actually think that's a good idea, especially when it's one of their newest and best ships out there. At best you allow Kirk to graduate early and assign him as the skipper of some small ship like a tug or tender, not the most glorious assignment but it rewards him with command while allowing him a chance to get more experience with being in command and all of the responsibilities that comes with being a starship captain. The movie could then end with Kirk being determined to work his way back to the center seat of the Enterprise and the sequel could, at the beginning, show him, some years later, having finally gotten command of the Enterprise and working on getting the band back together, so to speak. That, in my opinion, would both be interesting and dramatic as well as more realistic and, in a way, more keeping with the original canon while still being different.