Well, both the Atlas and Soyuz (currently used by NASA and Roskosmos) were developed primarily for the U.S. and Soviet militaries as ICBM vehicles, the Space Race was something of a PR operation.
After all, you don't really need to have an explosive payload: just dropping a heavy enough missile can be devastating.
Since kinetic energy increases with the square of velocity, if you can create a payload that can travel at hypersonic speeds (like a tungsten rod) without burning up then the amount of kinetic energy is in the tens of millions of joules. That's enough to destroy any single target, but doesn't have nearly the same destructive power as a nuke, which releases trillions of joules of energy.
According to the wikipedia article, the tungsten rods in question would be 9 tons and would deliver an explosion equivalent to that of 11.5 tons of TNT. Considering the cost of getting it into orbit, this is only a good idea when the advantages of the delivery method outweigh that cost. The advantages of "rods from God" compared to ICBMS are that they're twice as fast and have different dynamics vs early warning systems or anti-ballistic systems.
Sure, tungsten rods also work. What I meant was something far less sophisticated - "we don't care what specifically is hit, as long as it impacts in the general area." See e.g. the Qassam missiles, or similarly, the North Korean space program (or "space program"?) and Japan.
True, but unless you have hundreds of them, I'm not sure if it's useful for MAD (i.e. replacement for nukes).
I suppose if you made the tungsten rods heavy enough and made made them travel fast enough you could get kinetic energy on par with small nukes, but the problem is it's highly directional (i.e. most of the energy is released underground and absorbed by the earth), unlike a nuke which can release all of its energy at once in an airburst 100 feet above a city.
It would be useful as a PGM in the arsenal, but probably not enough for MAD in an arms race. I could be wrong, though.
I thought that limiting the GPS from the top was to complicate making cheap missiles, something that might be used by rogue states or terrorists; for MAD, you probably wouldn't choose COTS equipment.
After all, you don't really need to have an explosive payload: just dropping a heavy enough missile can be devastating.