Which would hopefully be detected in time to "solve" the problem, but still... ;)
Orbitals at predictable orbits and surfaceinstallations on airless bodies might be more in danger though. There even a well targeted fast crowbar might do quite some damage.
Faster then: the kinetic energy of such a mass moving at 12 km/s, faster than escape velocity, would be 'only' 137 tons of TNT, approximately 1/15th of the 2020 Beirut explosion. Even if you throw the rods into the ground at a blistering 50 km/s, that only gives you the equivalent kinetic energy of 2.4 kilotons of TNT, or 1/6th of the Little Boy nuclear bomb.
Then there are the terminal effects; such a tungsten rod is basically an oversized armor piercing dart like tanks shoot at each other. It will drive itself straight into the ground and most of the rod's kinetic energy will be spent pulverizing bedrock and itself. Such a weapon would be great for taking out bunkers, but I think very wasteful for any other purpose.
Wonder if it could be precision enough for non-military applications? eg possibly faster for deep geothermal drilling than using the existing surface based borehole drilling approach.
For military applications though, it'd wonder if such a rod (or small sequence of them) could be effective when striking geological fault lines. eg the San Andreas Fault line
Aka the old "use the terrain" approach.