“why doesn’t the military use something similar?”
Who says they fundamentally don’t? or use something better on general principle, which in doing so in no way detracts at the difficulty of breaking commercial strong encryption?
AFAIK, there is nothing compromising the security of RSA or better when using sufficient sized keys in normal usage.
Using ‘something similar’ means that it is at least one step above commercial grade encryption. If it above commercial grade, then commercial grade is broken - that’s how it used to work. What you postulate might be something used from one Central Command to another, if it exists at all and has nothing to do with my point.
“AFAIK, there is nothing compromising the security “ to my point exactly. If you do not absolutely know then it is speculation or opinion - if you do know then you have revealed highly classified info.