With the benefit of 11 years of hindsight, lets talk about Star Trek Into Darkness. Cards on the table: I don't like this movie at all. It's probably my least favorite Star Trek story across the entire canon.
While this movie was being promoted, no one would confirm that Cumberbatch was Khan despite rampant speculation. He's not even introduced as Khan, for the first half of the movie he's "John Harrison," and the Khan reveal is played as a big dramatic moment.
JJ Abrams' entire shtick is that he crafts "mystery boxes." So... is that it? Is Star Trek Into Darkness just a mystery box where the identity of the villain is the mystery, and Abrams & co. just worked backwards from there?
Lets be generous and say that's not it: Into Darkness had something to say. We have a conspiracy, a rogue admiral, an automated super-warship, the death of a mentor... it seems like we can pull something out of here, right?
... right?
Best attempt:
The story is mainly about Kelvin Kirk learning to be less of the cocky dipshit he still is at the end of '09. He's still riding high from his victory over the future Romulans, so he really doesn't respect the seriousness the Chair should command. You see this in the completely unforced error at the start of the film--Spock is (for some reason) dead to rights, and Kirk decides that the power of friendship is more important than the Prime Directive. Pike rightly reams him out for this, but the character thread really comes to a head when the USS Vengeance catches up to Enterprise and prepares to utterly destroy her. Much as I complain about the movie, I do like this little moment of helplessness from Chris Pine's Kirk. Staring down the larger ship's guns, Kirk can only watch helplessly and apologize for leading his crew to their deaths. It has the same vibes as Kirk from Generations--he didn't believe he was dying until he actually did. Obviously, the general thread of Kirk actually taking responsibility for his crew culminates in him doing percussive maintenance inside of the Warp Core and dying for Enterprise's sins. He gets better, but honestly I can accept this as the transition between cadet Kirk of the 09 and the actually quite competent Captain Kirk in Beyond.
Spock is the other big character in this movie. Sad as it is, this is the only real time we get to see Kelvin Kirk and Kelvin Spock's friendship explored in depth. They were at each other's throats for most of '09 and Beyond focused more on McCoy + Spock's relationship. Spock's friendship with Kirk is the main avenue through which they explore Spock's classic dilemma of his Human vs. Vulcan sides. As cynical as I am about them recreating the end of WoK in reverse here, I will at least concede that Pine and Quinto did well with what they were given.
Main complaint, besides Cumberbatch being Khan: they totally wasted Bruce Greenwood's Admiral Pike here. I'm of the opinion that Kelvin Pike was the best version we'd seen prior to Discovery, and probably did more than a little bit in reviving interest in the character. Here he gets stuffed in the fridge like half an hour in to make Kirk mad/sad. What a shame.
I love this take. Especially calling out the growth of the character. I've always seen the Kelvin movies as one trilogy, not individual movies. I never watched them individually which might help with that. If you see them all together you can really see the growth of all the characters. If they marketed it as a trilogy maybe people wouldn't be as bothered by it. I'm not super surprised that what I see to be the middle of the trilogy is the most disliked though. Most trilogies have this problem with the middle movie being vastly underwhelming to the others. Even the Star Wars Original Trilogy had that problem. When Empire Strikes Back came out the reviews were clowning on it for that reason. The story didn't really go anywhere.
Into Darkness feels like that to me. A second movie in the trilogy that spins its wheels on everything except for the character development. Nothing feels particularly awful to me, just sort of... okay. The only real problems I have is, as you mentioned, Pike being fridged almost immediately and how little buildup there was to Khans special blood. If you wanted to have the blood revive Kirk, go for it. I legitimately don't care. We've resurrected people for less in Star Trek and I'm more than happy to suspend my disbelief over the tech, medical or otherwise, in Star Trek. If you can turn into a salamander if you go fast enough or if spaceships can become pregnant, then you can do basically anything else. I'm fine with that. But there was no buildup for it. I think there's like two scenes from what I remember. One where Bones takes Khans blood and tests it and mentions that it's weird, and one where he injects it in a tribble. Basically zero attention drawn to it until the tribble randomly starts breathing again and suddenly it's a huge deal. If they had given like... 3-5 more minutes of random scenes throughout the movie of Bones talking about the weird blood or something I would not have given a fuck.