That is not killing it, that is embracing it. They would need to buy many bitcoins, I don't know what your definition of slowly is, but you are suggesting they would provide continuous demand for BTC. By the time they dump them, the markets will gratefully eat them and ask for more.
I think the point is that a government actor could most easily destabilize the BTC market this way, and in doing so, make it too risky to use.
A billion dollar market is a tenth of a rounding error to a large government, and if this was carried out in the name of "national security," the costs would be irrelevant (and classified) anyway. They wouldn't care that they enrich a few thousand people in order to shut down a way for evil-doers to finance their operations.
This is an interesting idea to play with, but IMO, highly unlikely. I think they are more likely to apply the necessary pressure to the weak points in the system in order to track and monitor the movement of large sums.