Or would you prefer a guy who looks 40 to be just a cadet who just signed up to Starfleet?
Bones did it. I see no problem with it.
Besides, Cupcake doesn't look 40. He looks more or less the same age as Kirk.
So IRL if a medic wants to join the army he has to do medical school all over again?
I don't believe that's the case, assuming Cupcake didn't have some sort of terminal-degree specialty.
McCoy (at least Abrams-McCoy) is a good example -- Already an MD and an older recruit, he completed his time at the Academy in 3 years as well, just like Kirk. I imagine that if he wasn't already an MD, he'd have to spend more time under Starfleet medical training (though perhaps not as a cadet or at the Academy).
But there's still a difference between on-field medical work and working in a hospital, e.g. being able to prioritize differently, working under fire, ability to command, working with alien physiology, etc. Thus, I imagine that if you're already an MD but you want to enter the Academy, you don't go through full-fledged medical school, but you still undergo some specific-training to adapt your skillset to a Starfleet setting.
I wonder if Chapel Prime (woot, love that name) underwent such a program: entering the Academy without a medical degree, but undergoing additional training while in the field and eventually becoming MD.