Hm. I think that Super Mutants could have actually performed pretty good in the military, given the context.
We are talking about a savage, wild war. Chemical weapons are to be expected : Super Mutants being immune to most bacterias and radiations would give them an enormous advantage, in this scenario. Their, er... diet would be an advantage too, if the enemy applies the old tactic of burning its own land to starve the invador. They could feed on the corpses and keep advancing : something that would have been Napoleon's wet dream, during the invasion of Russia. Which kind of looks like the invasion of China, in Fallout's lore, don't you think ?
And in the end, we have been trying to make obedient, super strong, enhanced soldiers in the real life, so the idea of the super mutants may not seem as crazy as that. There's the XOS2 which multiplicate your strength 17 times over and lets you lift 200 pounds several hundreds times without taking a sweat. We made Orexin-A, which gives soldiers the illusion of a night sleep, and potentially allows them to keep fighting for days straight. There has been the Project MK-ULTRA, which involved acid to erase memories of spies, in case they are captured. Nazis experimented with D-IX, which was basically a mix of cocaine, amphetamines and morphine to give their soldiers ultra stamina, tolerance to pain, obedience. And the worst part is that it worked.
In the end, Super Mutants are satyre of these cruel experiments to create super soldiers. But my point is : we tried to do this, in real life. For winning wars. So, applying that, the idea of super mutants is not "that" crazy, in a context of 50's wars, with foreign invasions, chemical and nuclear weapons etc.
As for using weapons, aren't Fallout's weapons bigger than in our world, so that they could be used by power armor units ? In which case, Super Mutants could use the standard US arsenal. I'm talking about the strange, cartoonish Fallout 4's weapons, though, not the ones in the old titles which seemed rather normal, except for the first handgun. Shame on me for using F4 as reference material.