I was interested in validating or invalidating the mach 4 number. I guess it depends on the specific rocket, but the 122 mm M-21OF-M Rocket, sometimes referred to as Katyusha (although that was the name of a specific launcher, not the rocket [0]) is 660 m/s or about mach 2 [1].
That's a good example of the problem. That's about 660 meters per second. Instead of "multiple seconds", the laser has about 1/100 second to penetrate the skin. Of a missile that's shaking, twisting, rocking.