In the Army, and most likely in other services, you only shoot your service rifle in two occasions - real combat and peacetime or other annual (or whatever that service requires for weapons firing practice) qualifications. The enlisted man has no choice of rifle or ammunition. He fires with his service weapon and the ammunition that is issued to him. Exceptions are members of marksmanship units where top shooter-applicants can get assigned to shoot in competitions, both military and civilian, and where match-grade rifles and ammunition are always used, trained snipers assigned to sniper units or practicing with other snipers (if they are assigned to units just as rifleman, which probably doesn’t happen anymore, they qualify just like any other soldier or did when I was in the service), and of course, the “dark side” of special ops, where they seem to use anything the want and that they can beg, borrow, requisition, buy or steal. Never was one of those guys, so don’t know all what they do.
When I was in by the way, Snipers were usually just assigned in each unit and picked for being the best shots in the company. They were issued the M1C or M1D rifle, but at that time I don’t know what ammo they were issued. They were NOT the super, highly-trained, incredible marksmen that comprise the snipers in today’s Army and Marine Corps. The sniper being a human shooting machine probably really had its start in the VN war, not that early snipers, even in the Civil War, didn’t get special training and special rifles. The M1Cs and M1Ds I have seen are not even National Match Rifles - they are simply standard weapons with scopes, although perhaps the barrels are picked for being closely-spec’d, I just simply don’t know.
One of the reasons AP ammo was used occasionally as substitute match when I was in the Army was the bullet weight, more than any other consideration. Matches had stages shot at longer ranges than what the normal “grunt” qualified at. Also, not being considered here is that there were local command teams that generally were only shooting in local competetions with other services with bases close by, or against local clubs. At Ladd AFB in the 1950s we had teams - the Ladd Army Rangers, for center fire and smallbore (also baseball, and perhaps football). These guys didn’t have the travel budget to go even to Camp Perry, where the Army was usually represented by a pretty select “Army-wide” bunch of shooters assigned to an AMU for that purpose. I actually made the Ladd AFB Army smallbore team, but found out my company commander, a company that I was newly assigned to and where I had a really good berth (ED from anything except “Charge of Quarters” - no KP, no Guard Duty) didn’t like “jocks,” that is, any one participating in anything that took him away from his normal duties. I had to pass on joining the team because as an 18 year old Specialist 4 (then called Specialist 3) which is a glorified Private First Class, I didn’t want to rock the boat on the cool deal I had in the company, since I actually was assigned only for quarters and rations. It was a Signal Company, and I worked, by then, in the Personnel Section of the Command Headquarters, having flunked my overseas Physical for eyesight. That being in peacetime, knocked me out of the Infantry (gee, I was SOOOOO sorry that happened).
Hope this helps to clarify the ancient picture of Army Marksmanship and arms and ammunition issue. My service started 54 years ago, so it is pretty much ancient history. Again, I can’t speak for what they do now but I suspect for the average, non-competition or “special” soldier (Snipers, Special Ops people, etc.), the principles are the same. You shot your issue weapon and issue ammunition, whatever they chose to give you (I qualified once when we all used AP ammo simply because it was getting old, in too much supply at our post, and they wanted to shoot it up). It was not my choice - it was what was issued our unit for that qualification.