For me the only role that a government should have crypto is the protection of it's users because people that are involved in the cryptospace is vulnerable to attacks everyday and the only way that I can think of is for the government to have a role as a protector of the users since they have the resources to do it.
Yes the governments can do a lot in this case. They have more facilities to work effectively on this field so if they will work then they will do it perfectly and they can manage to deal with these attacks and hackers. They can trace them but only they need to come and adopt this crypto.