It's weird, because a non-Trekkie would not know or care about the ages, where a Trekkie could not help but note a discrepancy. It seems odd to make Chekov really young and thus have to make him a whiz-kid to explain his presence at the academy only to pass with the fans, when fans are bound to notice the difference anyhow (those fans who don't care about the age won't care either way; those who do will hold it to be heretical violation of canon).
Might have been better just to make Chekov a person of indiscriminate age without having to inaugurate him as a super genius. This could potentially create problems down the road. Scotty is supposed to be the engineering genius, Kirk is the tactical genius, McCoy if not a Dr. House, is at least the highest medical authority on board, Spock is the science/all-purpose genius -- with Chekov as a another super genius it could get a little crowded. Who gets the epiphany? That question may have just gotten a little tougher. The genius factor also seems to potentially throw the Sulu-Chekov balance at the navigator/helmsman station a little off -- if Sulu isn't a genius, is he going to be a our go to fencing guy?
This isn't an insurmountable problem, but a complicating wrinkle - another thing you now have to keep track of, unless of course all reference to it is dropped in later films. In that case it just becomes a vaguely felt question "Hey, wasn't Chekov a genius in the first film? Seems like he should have some ideas here..."
It's interesting how when you move the narrative furniture around even a little bit the details quickly ramify.
I think this is evidence that this Chekov is not the same biological individual as in TOS, although it's entirely possible that he has a younger brother who is. TOS was often portrayed as a bit of a buffoon, although he was a mine of scientific trivia. He was no genius... Chekov was a scientist with evidence of him having a background in zoology, astronomy, atronavigation, and planetary sciences. Sulu was a physicist/astrophysicist with an interest in botany. They also made Chekov a security officer in TMP, despite the fact that he was ill suited to that role (often getting beaten up) although he made a competent bridge tactical officer.
I prefer characters to have their own niche where they can shine but those areas usually get bumped for a) convenience and b) to give Kirk and Spock the most air time.
They do seem to have an awareness of character niche hence Sulu got to go sword fighting. Chekov's niche is now different (maths and transporter use) for the sake of convenience but I can see that his becoming the go-to guy for tricky transports gives him a niche.
It's a shame though, Janice Rand became a transporter operator in TMP and that could have been her niche. She has a history of killing people on the transporter so losing Amanda would be right up her street