Yeah one reason I think the government has to offer this is usability. While you can imagine a purely p2p protocol between cypherpunks, for everyone else there needs to be a way to social workers, DMV staff, etc can deal with edge cases (such as your id being stolen and needing a reset). Furthermore it helps if it's super illegal to tamper with this network (consider how rare check fraud is, despite being easy).

Check fraud is easy to commit but not easy to get away with while also benefiting financially.

It's also illegal to steal things but that happens much more frequently because it's often fairly easy to get away with.