You might enjoy Elizabeth Warren's proposal about designating "platform utilities":
https://medium.com/@teamwarren/heres-how-we-can-break-up-big...But that aside (and I think she's using "utility" in a slightly different way), I think it would be a huge mistake to say that our approach is to regulate Twitter (and Facebook, and so forth) as is. That just cements their oligopoly: either your regulation calls out these companies by name (and therefore needs to ensure they retain power to work), or it imposes a regulatory burden which makes it even harder for competitors to replace them. This would be a serious unforced error for people who think that Big Tech is run by their political/ideological opponents. It would also be a practical disaster (imagine government-regulated Twitter spam detection), and IMO it would reflect an abandonment of the ideal of liberty. Rather than providing some structural reason why we need to regulate Twitter, we'd be regulating them baed on their effects - that they did something we don't like, and we don't know how to stop it other than telling them to not do it. It feels like it violates the spirit (though probably not the letter) of the constitutional ban on bills of attainder.
A sibling comment points out the "natural monopoly" argument for regulating ISPs as utilities. That's an argument on structure (there can only be so many ISPs and there's a huge up-front cost to becoming competitive), not effect, and in fact the argument for Net Neutrality was that companies could act in unwanted ways in the future, not that they did.
Our fundamental model for Twitter should be that it's just a company, and it could be replaced by some other company, and if we think that's infeasible, that's the bug in the market that we should fix. We should not resign ourselves to some government-guided-Twitter monstrosity - either you get regulatory capture or you get a private company whose product priorities swing with every election. My personal thesis here is that Twitter is simply too big, and that companies should be barred from growing beyond a certain size (of revenue, employees, or some similar measure). We can break them up like we broke up the trusts of old, and in fact like the trusts of old, they'll probably generate more GDP broken up - without the giant incumbent distorting the market, there's a more meaningful and direct profit motive on each resulting piece as well as more room for innovation by new companies, and therefore more general room for economic growth. That would be regulating the structure of the market in a generic way, and it would specifically regulate it in a way that promotes the ability of the non-government parts of society to have primary responsibility in shaping society.
There is an alternative political model where the government is closely involved in making sure that social media is run in a way that promotes the society the people want (in the government's opinion). WeChat and Weibo run under this model. That model seems to be unpopular in the US (I recall something recently about trying to ban WeChat), and I hope we don't decide that they had it right all along.