Social networks tend to kill each other due to network effects as people are flocking to the most used network since there's the largest value for everyone. So having multiple networks might not really work well.

It wouldn't have to be several networks though and it doesn't even have to be your own government running it to provide the value you're looking for (social networking without users being monetized).

Image for example Twitter being bought by a country with good reputation, strong privacy laws and sufficient economy to sustain it in the long term. Iceland with some additional funding from the EU or something like that.

Does not sound too bad, in my opinion.