Let's also remember that in peacetime eras of Trek it's made clear that there's incredible competition just to get into the Academy.
One of the things about TOS is that it isn't obvious that the majority of the officers even went to a academy. Kirk, Mitchell, maybe Spock and Chekov.
In TNG/DS9/VOY there's usually dialog at some point informing the audience that the majority of the main characters we see are academy grads, not so with TOS. McCoy didn't go, my impression is that Uhura might have come up through the ranks, I could easily see Scotty being a OTS type.