Banning no, but regulating yes. You used to need (or still technically need) a broadcast license or something to broadcast news or public a news paper. So historically this would have been the default, that if a newspaper publishes hate speech or derogatory lies about a person, that they can be legally stopped from doing this. All that went mostly out the window for social media, who have taken over news "reporting" and political commentary, replacing it with algorithms that act purely for profit and deliberately create divisions and polarization. The government absolutely has a duty to protect adults from that. Addictive substances have also been outlawed / regulated.

It's just that when all this started it was small and harmless and most computer nerds were very much against any kind of regulation. We were warned but I was an idiot back then too. Now we have an overwhelming concentration of global political power in the hands of e.g. Zuckerberg and others controlling social media, for profit, for neoliberal political goals, for the suppression and diversion of political expression, or promoting fascist political ideology. It's really only since ~2010 with Trumps rise and backlash to Obama that things quickly became this bad.

We are supposed to be a democracy, but today unchecked foreign political power not just influences the opinions of people, but sets the agenda.

I would absolutely be in favor of banning all unregulated (e.g. US) social media and creating an EU wide public utility social media network. Just make reddit, facebook, insta and all that stuff inaccessible in the EU unless they comply with very stringent regulation and moderation and a "non-profit" approach. China and Russia have their own media not just to suppress dissent, but to protect themselves from US influence. But I do think we now know enough to create a better alternative than either.