The Saturn V was simply a scaled up V2. The critical components were all there:
1. boundary layer cooling
2. pre-heating fuel and cooling the nozzle by pushing the fuel through tubes in the nozzle
3. baffles to prevent pogo-ing
4. turbo fuel pumps
5. supersonic airframe
6. guidance system (although primitive)
The V2 was an ineffective military weapon that did little damage - because its guidance system was too primitive to be able to hit a target. Hitler also poured enormous resources into the V2 program, shifted away from producing weapons that were effective.
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.
https://en.wikipedia.org/wiki/V-1_flying_bomb
So it is about the big picture. (And about small pictures like that of Elon making a salut like the other group).
So yes, currently his rockets do not transport explosives. But that can change anytime and I expect it will very soon.