At least they made an attempt to explain the unbelievable coincidence.It is all about presentation. If Spock Prime had found Kirk's pod after it landed on the planet, I would have been okay with that. If Kirk had gone to the Starfleet base and Spock Prime arrived after him, I would have been okay with that too.
But Kirk being chased into the cave by a giant monster and Spock chasing it out with fire?
It takes a "special" mind to come up with something like that.
Like Harlan Ellison and Gene Roddenberry?
Spock: "There is a theory. There could be some logic to the belief that time is fluid, like a river, with currents, eddies, backwash. "
Capt. Kirk: "And the same currents that swept McCoy to a certain time and place might sweep us there, too?"
My point was, that similiar "currents" swept Young Kirk and Spock Prime to one another.