Should we nationalize social media platforms?

Should Twitter and Facebook be regulated as public utilities? There's been a lot of talk about Twitter banning people because of their opinions, but as a private company, they have the freedom to do that. If they were regulated by the government, then they would become de jure public spaces and would be subject to the first amendment, thus no more banning people because of their opinions.

Given the influence these sites have on politics and elections, maybe it's not such a crazy idea.