It is certainly not going to be easy by governments to remove privacy coins out of the crypto economy. There are actually individuals, organizations, company, who needed privacy on their various activities, and naturally man has some elements of privacy in everyday leaving because of the unknown.
Again, governments knows the importance of privacy, even though they will like to act as people vested with authority and power. It is then important to note that privacy is a right, though some people will like to abuse this right, working different kinds of mischief and ilicit activities, but privacy is part of life.
In addition, i think privacy coins will continue to exist, because, even government itself has some private activities, and besides the fact that they are governments, they are humans, though operating as a body.