The system would also have to cope with atmospheric heating from re-entry, which could melt the weapon.
Then there's the question of whether or not heat is truly the most immediate issue. NASA and USAF had to actually fly an airplace near and past the speed of sound to see how the properties of the atmosphere changed when compressed. Is it logical to hypothesize that similar changes may be encountered as speed continues to increase?
(Still, there are plenty of configurations that make good kinetic-kill weapons with a manageable amount of re-entry heat. Think large rods with good amounts of mass and small cross-sections. This is an engineering problem, not a show-stopper.)
If I did my math right, that's the energy in a 400 megaton bomb, or 17 kg of antimatter. The US nuclear arsenal is about 2500 Mt.
I don't think you'll be able to distribute that much energy so uniformly. Almost certainly you'll end up with all of it dumped into the surface, with people, land, and cities burned to a crisp. Only a few people in mines or deep valleys might survive.