Gravity is not your friend. Getting stuff into LEO is still expensive af. A kinetic projectile dropped from space might have the same energy as a nuke, but it’s still going to be a lot more expensive. Additionally, you don’t have options on how that energy is released. It’s going into the ground and that’s that. A nuke (or any other explosive device for that matter) on the other hand can be detonated at a chosen altitude, or as a bunker buster if that’s what you want.
The heavier the object, the more it’s going to take to push it out of that orbit. If your weapon system is in LEO, you can realistically only drop a rod on a small envelope along the future trajectory of the weapon system. Polar orbits would have the best coverage, but fly over a target outside of polar regions only twice a day. In order to get a wider range of firing solutions, the projectile needs considerable deltaV for orbital changes. And again, gravity fucks you over here because deep within Earth’s gravity well, changing the orbit of a massive tungsten rod takes a lot of fuel. Higher up these deltaV costs wouldn’t be as prohibitive and you’d have more options for using the weapon, but that would increase the time from launch to impact into the regieme of hours, way too slow for anything.
The best solution would be to have a huge amount of rods in different orbits (akin to the spacejunk that is Starlink) to maximize the chances of at least one being able to fire on a target at any given place at any given time, but because those rods are still heavy af, such a plan is completely unfeasable.
Rods from gods will never happen, at least not around Earth.
I have my doubts about that stealth. If it were just the tungsten rod by itself, it could well be coated in black, but the impulse needed to drop a massive projectile out of an orbit (and furthermore into a trajectory that impacts at the target) necessitates a relatively hefty maneuvering unit and that has to radiate heat to be kept operational. Cheaping out on the propulsion could be very costly because a failure in the middle of the deorbit burn would result in the rod coming down in a place you don’t want it to.
The only way to hide it would be with decoys, which are already used by ICBM’s. Unlike ICBM’s, an orbital platform would need those decoys well before it’s used because there’s no terrain to hide in. A ballistic missile sub is very hard to track, satellites, not so much.
About countermeasures: Becuse the rod can’t move by itself, it’s stuck on a fixed trajectory after the propulsion stage is discarded. This makes it an easy target for an interceptor missile. You already know where to look so the stealthy rod isn’t that hard to find, and then you just have to collide with it. And because the rod is coming down from MEO at the very least, you have ample time to do all this. An impact at such speeds would disintigrate anything and the rod isn’t an exception. At the very least it would fracture into multiple less aerodynamic pieces that do much less damage than the sum of their parts.