I had to watch parts of it again. Captain Pike says to Kirk he has the instinct to leap before he looks like his father. So Kirk taking risks wasn't because of the events of the USS Kelvin. Therefore he wasn't any different from Kirk Prime
The degree to which I would argue KT Kirk was more risky. Prime Kirk had been tempered in his more traditional rise. Where KT Kirk was more over the top.
where the Enterprise saved that air force pilot after his fighter was caught in the Enterprise tractor beam. They were going to keep him until they found out his future son not born yet played an important role in history.
another trope in trek "Unhappening"
Tommarow is Yesterday "unhappened" when the Enterprise back tracked over its own time travel. They beamed Captain Christopher back into his cockpit and used the transporter to ensure that his jet didn't crash. All he would have been left with was his own memory.
Infact much of trek Time travel is controlled or corrective where the crew is sent to fix something gone wrong.
The Voyage home is a trouble maker but Enterprise crew did at least try to cover themselves.
Still a case by case on the outcome.
Plexi Corp ends up with the chemical formula for transparent Alluminum for the low low price of a 6' thick 40"/10" pane and a joy ride on there Bell 204.
Results: leave it be. We know that it would take years to figure out how to make it and Plexi Corp may Well have been the patent holders in the end. After all in our own timeline ALON sure enough shows up a decade latter.
A seemingly unwed female citation Biologists disappears after a fight with her boss.
Resuilts: Leave it be. People disappear all the time. She was witnessed dating a odd gentlemen before the events, suspicious or could have easily been the results of depression brought on by the loss of the whales. A huge part of her life. Still it would be a year before an investigation.
The Navy has questions about a break in on the CVN65 capturing a suspected Russian operative who then escapes without a trace from a hospital. His personal effects are the most dangerous elements a Klingon phaser and Communicator.
Results: trouble spot! The phaser and Communicator are advanced technologies. The US DOD would have taken then for farther study. Fortunately TOS has a possible solution Gary Seven Supervisor 194 would likely have removed the devices having detected them on earth. His Job was to ensure Earths evolution went the right way.
A Norwegian whaling crew has the heck scared out of them and tells the biggest fish story you ever heard.
Remedial action: leave it be. No evidence just a story.
And two Humpbacks that where about to be harpooned disappeared.
Remedial: Leave it be. They were about to be killed by the whalers. As far as the world is concerned they were.
City on the edge of forever is easy.
Edith Keller's death was a forgon conclusion that was only made possible by Kirk, Spock and McCoy.
It was the Depression. People came and went all the time.
Star Trek travelling back in time doesn't change things automatically from the start.
The closest event to what happened in 09 I would argue is Star Trek First Contact.
When the Borg went back and assimilated Earth. But the crew of the Enterprise E went back to and stopped them. But before the Enterprise traveled back they saw an Assimilated earth.
The Destruction of the Kelvin however never had a correction.
No Enterprise E to follow Narada back and destroy her before the Kelvin encountered her. This is why the ramifications for the timeline were massive.
Kirk was originally born in Iowa suddenly he is born in space. He also didn't witness the events of Kodos the Executioner nor was he a phaser operator on the faragut. He rebels against his step father well his mother is away earning him a criminal record. He didn't Join Starfleet as a legacy but needs to be pushed to it a few years later by Pike. He is Brasher Bolder more cocky and full of himself. The Prime Kirk is a bit of this but he also restrains his Leap before looking mentally. But it's only awakened by a Friend Gary Mitchell in the second Pilot Where No Man Has Gone Before.
Second the crew of the ship that died in battle were not supposed to at least not there.
The Kelvin was a big ship with a larger crew. Based on the math of Prime Kirk vs KT Kirk it's likely that they were on there way home and its suspected that Kirk's Mother was about to be placed in Stasus for the last few months of pregency.
But then the ship is attacked Kirk' s father is killed.
Third the Starfleet command suddenly were told that not only were the Romulans back but they were bolder and brought out a monster ship. By that point the Earth Romulan war was just 60 Years old. During the conflict the Romulans has been keen on keeping there faces a mystery. And at best seemed a match for Earth's forces.
Now a Apparent Romulan ship that rivals starbases, shows up and blatantly attacks easily overpowering the Kelvin, makes open communications.
To Starfleet the Romulans suddenly shifted from subterfuge to all up on their grill. It's a black ship type event. Going from no contact for decades to BOOM. It would have hit the Federation like 9/11. Starfleet would have shifted priorities on a dime pushing to try and match this new threat. Reinforcing for an invasion fleet bulking up what it had Delaying the new cruiser class they had on the books as it would have seemed absolutely obsolete vs this new threat. And then... nothing. No invasion no follow up. The Romulans apparently keep quiet. Starfleet is weary and places more security around the Romulan Neutral zone as a result the Klingons fell less threatened or perhaps more threatened by the Federation. Either way the war doesn't happen.