Kirk is 25 or 26. In the TOS he was 34 when we met him and had been in command for some time. The field promotion culture is similar to what happened in WWII so it is not completely off the rails.
Not even in WW2 would we have had a 26 year old in command of a heavy cruiser-class ship, so that's stretching it quite a bit. I can see wanting to have a young crew so the franchise can be stretched for a couple of decades if this works out.