Istrebitel Sputnikov (Destroyer of Satellites)
KKV’s make a lot more sense if you’re trying to hit a nuclear warhead, which might be intercepted in or out of the atmosphere.
High MACH atmospheric friction would significantly degrade the effectiveness of the shrapnel type warhead.
Good Wikipedia page on ASAT’s including the US F-15 launched ASM-135 ASATand the Soviet Istrebitel Sputnikov