Without a doubt there are going to be a huge number of replies where posters report MOA and sub MOA groups with military surplus ammunition. I expect to read of three shot groups, five shot groups, maybe a 10 shot group, but I predict, there won't be any MOA or sub MOA 20 shot groups.
I pulled MIL C 1313F Cartridge Caliber .30, Ball M2, dated 1971. The accuracy requirement at 600 yards is that the mean radii shall not be greater than 7.5 inches. The diameter of the group will be double that, 15 inches, which is over 2 MOA, but, others have stated a reasonable extreme spread to be three times the mean radii. I don't know how to exactly convert mean radii to an extreme group size, without the group data.
But lets say the mean radius converts to extreme spread by multiplying the mean radius by 3. Then the 7.5 inches at 600 yards converts to 3.75 MOA. And that is reasonable for military ammunition. In the book "Hell to Pay", the statistic of 65,000 causalities per month was experienced by the United States Armed forces during WW2. And that works out to 5000 dead per week, the remaining are alive, but in various states of disassembly. By the fourth year of the war, guys are being sent to the front with minimal firearms training. Two guys with whom I talked about this, one had a total of 20 rounds of live fire before landing at Iwo Jima, my Uncle 101 Airborne, had eight rounds of familiarization with his machine gun before dropping over Normandy. When soldiers are being used up at that rate, and training is so rushed that at best the boot understands how to disassemble and clean his weapon, expecting world class accuracy from the draftee is unrealistic, and ammunition and weapon standards can be relaxed to increase production. It is far better to hand the Solider a weapon and ammunition that goes bang, than promising him the most perfect combination of ammunition and firearms later. After the landing sort of later, just rush the beaches with pointy sticks, overwhelm the enemy firing Nambu's, and if you survive, you will get a target rifle and target ammunition later.
As a general rule, 3 MOA is pretty good for a military rifle and its ammunition. And, finding someone who can shoot 3 MOA in a combat situation, is also pretty good. And in a big war, finding someone who lasts 9 months in combat, is pretty hard. They happen, I have read their books, but, look at the number who did not make it. I had another Uncle, died within 20 days of entering the European theater. He was a replacement, managed to join his unit during the Battle of the Bulge, and he did not make it out alive. That was pretty common.
So, how accurate does ball ammunition need to be? It can be more accurate than requirements but it is a stupid vendor that reduces his profits by spending time and energy trying to improve on the spec.
You will see confounding things. These IMI bullets will barely hold the black in my 308 Ruger M77, but shot unusually well in a M70 Sporter.
This may be a statistical abnomally. The bullets are mil spec, the cases and powder also, but they were my reloads. I have not tried a larger group I was just blowing bullets down range to zero a scope.
I did shoot 17 rounds with the old military match bullet. And this is closer to what I expect for the old bullet.