One important reason is the "cool" factor. Anything that's associated with the government is uncool by default.

Not to mention everything else - privacy, state surveillance, network effects.

If there's free choice, I don't see the general population ever choosing a state-funded network over private ones.

One way to do it is for the state to take significant control over an existing private network. Another way to do it for an authoritarian state to block all networks and make it mandatory for citizens to use the state-funded network.