Kirk in TOS was so ridiculously young for his job that they made a point of it in the writers guide.
What, you didn't notice that every other starship commander we saw in the series - other than Pike, the proto-Kirk - was greying? Tracey, Wesley, Decker...
As for Chekov - it's just a movie. Chekov is Chekov, that's why he's there. This kind of hair-splitting is like the old joke about the historian who tried to prove that Hamlet
wasn't written by William Shakespeare, but by another guy named William Shakespeare.