Let's look specifically at just the US for the sake of simplicity: The idea of the Internet in general as a public utility has only very recently become accepted and is still going through growing pains. Even so, the total percentage of people in the US who use the Internet is "only" around 84%.[1] Of those people who use the Internet, around 24% are Twitter users.[2]
If Twitter were to simply vanish overnight, the large majority of people in the US would be completely unaffected. I'm not sure you could say that about any other public utility.
[1] http://www.pewinternet.org/2015/06/26/americans-internet-acc... [2] http://www.pewinternet.org/fact-sheets/social-networking-fac...
If Twitter disappeared tomorrow, most of the public wouldn't bat an eye.
As far as I know capitalism hasn't yet come up with an answer to the question about how to privately finance infrastructure without making it so expensive that a large portion of their users have to be excluded. (See public baths, railroads, sewage-systems etc.)
Maybe not everything that is useful can be turned into money.