In a world where spying on civilian communication of adversaries (and preventing spying on your own civilians) is becoming more critical for national security interests, i suspect that national governments would be lighting more of a fire if they believe their opponents had one.
They absolutely are. NSA is obsessed with post-quantum projects atm
tbh they could just be pushing for people to adopt newer, less-tested, weaker algorithms. switch from something battle-hardened to the QuantResist2000 algorithm which they've figured out how to break with lattice reduction and a couple of GPUs like those minecraft guys did.
But is this because they are already needed or because they want to preserve encryption for past and present data post-quantum?
The latter
NSA is pushing for PQ algos.