The desire was obviously to bring all seven TOS movie characters back to the big screen. That required one retconn, Chekov's age. Not the biggest deal, really. If he had been in uniform at age 13 or 14, I think everyone would've had a cow.
As far as him being some kind of whiz kid goes, in TOS it did seem as if he was being groomed for command and moving along the path rather quickly. He was navigator, sometimes a science officer (or at least manned Spock's station on the bridge), and then started to go on landing parties. By TMP, which was only three years after the end of Kirk's first five year mission, he was head of security on the Enterprise even though he was not yet 30.
It's really too bad they (writers and producers) didn't continue his growth and let him be the captain of the Reliant in TWOK. It wouldn't have required that much re-writing to do it. Just make Terrell his first officer and not much else in the story has to change.
Koenig was actually eight years older than Chekov.