Why not? If we ever reach the scenario where bitcoin is being used by anything even approaching a large number of the global population, can governments afford not to mine? If a good chunk of international trade ends up being conducted using bitcoin, are governments going to be happy not having a stake in the security of the network (never mind not earning more bitcoin for themselves)? If a chunk of US trade is happening in bitcoin, and the CCP in China start mining bitcoin, then the US government will almost certainly set up their own mining operation in return, for example.

And that's of course assuming that people are mining with electricity from the grid, and not just hooking their miners up directly to their solar panels/wind turbines or other means of renewable generation.