TOS Chekov was science trained and I think it's a shame that they couldn't find a way to remain truer to the original character in NuTrek. I can live with him being trained as an engineer instead but my problem is just the rapid rise to chief after only a year as a qualified officer on duty in a different department. I do understand why they wanted to give him more do do but that was a silly way to do it.
Remain truer to what, he wasn't exactly fleshed out in any meaningful way in TOS. The most general audiences remember is that he's the one who talks funny.
I've got a cast of seven main characters, two antagonists and a new science officer that I have to work into the story and I have two hours to do it. Under those storytelling constraints, I have no issue with Chekov being handed the chief engineer duties.
In the real world I still don't have an issue because of familiarity. I hate to say I did exactly what we're discussing here because I promoted a lesser qualified candidate because I had worked with the lesser qualified candidate and was comfortable that person could handle the job better than the more qualified candidate. It's never as black and white as you'd like to make it sound.