It's been touched on - the military does not issue a sidearm to one and all, it's based on MOS an1d the unit's MTOE. They only have enough for those who are assigned to have one. In a support company, maybe one or two for the Company Commander and 1SGT. In an MP squad, 11 sidearms, 11 M4, possibly 11 shotguns, plus M243's, Mk17's, and M2's enough for every vehicle. MP's are more heavily armed in the Army than any other unit.
And we used them, regardless of age. However, end of duty, they were US Govt property, they went back into the Armory for the next shift, and taking them out and turning them in was NOT part of the shift time, it was in addition to the shift. If you worked 8 pm to 6 AM, you showed up two hours early and got away from the armory two hours later to accommodate drawing you weapon and ammo, then turning it in, plus vehicle maintenance and transportation time to get there on time no matter what.
So, 14 hour days can be quite common. Therefore we worked 3 on and 2 off just for the privilege of carrying a sidearm, whether someone was under the age of 21 was a bonus - young, healthy, no broken joints, and a uncluttered mind with clear vision and no complicated nuances about the quirks of law.
Carry on duty is pretty much black and white, you know exactly what not to do. I'd sooner trust a 19 year old who's gone thru MP training to carry anywhere he wants to, than put up with some other 19 year old who thinks he can drive better than Mario Andretti. That track record is already carved in stone, the insurance premiums are completely justified. And because of that, we impede the rights of the younger guys who are qualified so that the stupid ones aren't a problem. There are just too many.