Chekov Prime was ill-equipped to be security chief too (he was naive and more interested in scientific trivia than security protocols and he was always geting beaten up)
I think you're overlooking that there's a gap of several years between when we last saw him as navigator and when we first saw him as security chief. He could've spent the years that the ship was being refit undergoing extensive security training. (There's a novel, Traitor Winds
, that shows exactly that, exploring how and why Chekov made the transition to security.)
I love Traitor Winds - it was the first novel I read where the focus was not on the Big 3. However, I was referring more to how Chekov was portrayed in the movies after TMP. He was assigned to the science department in TWoK and there was never any real evidence that he was a competent security officer in TWoK, TVH, TFF, and especially not in TUC. Look at scenes like the confrontation with Khan, the interrogation on the nuclear wessel, and the murder investigation. As a security officer, he looks shambolic.
Now NuChekov can be painted differently and if moving him off navigation opens up a slot for a new minor female character (I'd love to see them make use of Ilia, even if they just use a bald bit part actress). However, making the boy genius a combat expert feels like an odd fit.
I also have to 'fess up and say that I've been a proponent of updating Janice Rand as a security-trained yeoman in order to provide a simple role for an action heroine, so updating characters is not something I'm against. To a certain extent though, the horse has already bolted for Chekov.