Except Chekov is the one we know is a different age, about 4 years older in nuTrek... but since his birth is after the timeline change, that's allowed. But that means nuTrek Chekov is not actually oldTrek Chekov. A different kid with the same name born to the same parents but at a different time.
Either that, or he was lying about his age in "Who Mourns for Adonais" for some reason. Or he was using some other planet's years rather than Earth years.
Although I'm inclined to agree with the "cross-temporal older brother" theory, because Chekov Prime never seemed to be anywhere near as much of a genius as his counterpart.
Or it might be that a point was just never made of it in TOS (no one calling him a whiz-kid). Otherwise, Chekov did seem able to fill in for Spock at the sciences station when he wasn't on the bridge (even though he was in Command, he also might have had a background in Sciences).