Big tungsten rods don't make sense. Very massive to put into orbit. Bothersome to de-orbit. Problematic to guide to target. Overkill for ordinary targets and not as effective as a nuke for extraordinary targets. Tungsten from space? As long as we are unicorn-farting, why not platinum?

Unlimited budgets don't exist. A ballasted conventional re-entry vehicle with radar homing (think Pershing II warhead) could probably sink a battleship. But as an orbital weapon, you would have to wait until the orbit track crossed the target and the timing was right. Why bother, when a ballistic missile can do the job without waiting? (It doesn't get you "close" to your target. You have to drop from orbit thousands of kilometers upstream.)