In the real world we so far just managed to keep space free of military weapons not because they are expensive, but because of treaties. I just don't expect those to last much longer.
And frankly I never looked into the concept, but why do you think, a space base tungsten penetrator would be way more expensive, than a nuke on a missile?
The idea as proposed in various places is a very large multi-ton vehicle. He chose to focus on trivia. Pretty common for Elon fans.
Humans are pretty clever at devising ways to kill each other. The Russians put a garbage can of concrete on a ersatz ballistic missile on a terror strike against Ukraine. Like you said, these things don’t exist because of treaties.
That vehicle could deorbit and drop a tungsten penetrator, smallpox, a nuclear device or any number of things.
All funded by a combination of government spending and defrauding the public via the Tesla Ponzi scheme.