This technique is also used in Peter F. Hamilton’s Night’s Dawn books. The rods were delivered by a starship diving towards the planet at high speed so they were already going really fast before encountering the atmosphere.
Geostationary orbit is at 22,236 miles.
Your math is right, but the point of a weapons system is not to exchange X joules of energy for greater than X joules later. It’s to destroy something in a way that gains a military advantage.
If a kinetic weapon enables you to destroy an enemy’s nuclear deterrent without warning and the possibility of a retaliatory attack, it’s worth a thousand space launches. It may be expensive, but it’s a lot cheaper than a North Korean nuke incinerating Tokyo.
Planes and such are cheaper, but are detectable, and can be seen from much further away than it takes to launch an ICBM. The point to Rods from God is the surprise factor. That’s worth billions if you can do it - hell, trillions. The entire point of the Cold War arms race was a race to threaten the other side’s deterrent capability while retaining one’s own.
Geosynchronous orbit?
Why the telephone pole shape? I find it hard to believe these things can be aimed with the accuracy needed to concentrate the force of impact on an area less than one square foot.
My guess is to limit the velocity loss on entering the atmosphere- less drag, and all that.
Seems like these things would be hellacious bunker busters, and wouldn’t be nuclear in the bargain.