Two words depressed trajectory.
Not only is it much faster than a ballistic trajectory the response window for exo and especially endo atmospheric interceptors is drastically reduced. With MARV warheads it’s effectively impossible to intercept a mach 12 MARV that is pulling 100+ G turns in the 30 seconds or so it’s above the radar horizon inbound.
The USA tested the MK500 evador warheads package in the trident right before the cold war ended it was viewed as such a capable first strike weapon it was never fielded since its sole purpose was first strike against hardened targets with a CEP measured in tens of meters which puts even a 5000 psi silo inside the fireball where even concrete is vaporized by the 100+ million Celsius thermonuclear fireball.
https://scienceandglobalsecurity.org/archive/sgs03gronlund.pdf
And yet this video that people claim is the Chinese launching a missile shows the missile going up into a ballistic trajectory and not the flatter trajectory that your scenario would require.