Those are all good questions Cadet49
. I'm thinking we may not see the wrestling itself (on film) but we will see the man it makes him. There will probably be some reflection shown, assuming the next movie is less full on action. When he's being dressed down by Pike he's like a cocky school kid in the principle's office.. I don't think we will see that again. Prime Kirk is brimming with confidence but it's tempered by experience and we just saw NuKirk get that experience.
And really he was the perfect fall guy for Marcus, already under suspicion with discipline issues. He couldn't send say, Bradbury, out there because Bradbury was a much older man. Giving the mission to the loose cannon would enable him to shift the blame very easily.
And yeah Kirk should feel like shit because of this.. but it's not like it would have gone down any better with another Captain.