There were armed variants like the YF-12. So far as I understand, the main reason the game changed is because missiles improved. Not much point focusing on things like speed when some missiles are reaching mach 16, contrasted against the SR-71's mach 3.3. In that context you simply have to pray your counter-measures work, and if that fails, then hope your ejection seat works.

Bullets are slower than the SR-71 - it would shoot itself down if it had a gun.

Newton disproved that more than a century ago.

Did you mean Einstein? But it was only a “thought experiment” …

I was wrong, it was actually already Galilei: https://en.wikipedia.org/wiki/Galilean_invariance

who described that a motion happens in relation to its inertial system.

Fact is, the claim that the SR-71 would fly into its own fired bullets is absolutely ludicrous.

« claim … ludicrous » — Without knowing much about physics, I totally agree.