The people in the military presently carrying sidearms, except base LEOs, are those who "don't really need them" (officers), or those who should be carrying some type of more capable weapon (security).
The rest should have the ability to secure at least their own safety or better, to use a sidearm as intended, to "fight their way back to the rifle they shouldn't have set down."
The elitist idea that rank and file military cant be trusted with a pistol is asinine. This idea was born from the tradition of sword and pistol representing status of a noble in command and has no place in a functional modern military.
If Im supposed to trust an individual to drive a tank, fire artillery, fly ordinance over my city, or protect my Secrets, then I can trust them to carry a sidearm.
Those who cant be trusted SHOULDNT BE IN THE MILITARY and need to be booted.
While I admire the way you think that's a bit impractical for a number of reasons. In most, even 99% of cases, the issued weapon is the M16. Only medics (the Navy has corpsmen) and in some cases, aviators, tankers and some officers (staff usually) are issued sidearms with which they have to qualify. It's nearly impossible to lug an M16 around daily especially to the office. Imagine leaving your rifle in the latrine (the navy calls it the Head and civilians call it the bathroom) where any janitor could find it.
I was an officer in an infantry outfit. Guys like me lead the killers in their duties of knocking off the enemy. Don't tell me I don't "need a sidearm!" I was also Executive Officer of the post pistol team (second in command) for a time. Back in those days, when General Dozier was kidnapped over in Italy by terrorists (later executed) my bosses who were the Division Commander and his key staff ordered all division staff OFFICERS to come to work after drawing a sidearm (1911 45acp) and at least two magazines of ball ammo and wear said sidearm under the duty uniform, concealed. When the division HQ building was hit with a bomb threat, they evacuated and then sent all of us LIEUTENANTS back inside to look for the "device!" It sure made me feel special, I'll tell you. Special and decidedly expendable.