Regardless of the Phantom's rank, even if it was a Second Rank Phantom, the government always had missions ready for it.
Sure, if it were a K4-Phantom, and even more so a Second Rank one, the government had much less leverage than it did over weaker Phantoms.
If the government needed it, they could force any K0-K3 Phantom to do anything. Some needed only slight pressure, others needed more, but in the end, the result was always the same.
This stopped working on the K4-Phantoms.
Why?
Well, the government simply had nothing to threaten them with, as the K4-Phantoms understood how valuable they were to all of humanity. Moreover, most of them had nothing to lose, because they knew that all they would have left after the World Wipe would be their Operators and friends among other K4-Phantoms.