The entirety of the internet is not composed of private entities. There are plenty of public entities that comprise parts of the internet. (And, in the US, those public entities are restricted in viewpoint discrimination when they create public fora.)
Now, it's true that private users in the US generally must deal with private vendors for internet services, and most of those services (including, e.g., DNS services) are neither public nor regulated-utility services, which does mean that lots of things one might want to do on the internet are subject to viewpoint discrimination by other private parties whose collaboration would be necessary for one to complete one’s intent.
> Should we simply stop expecting anything resembling free speech on the internet?
Free speech involves, fundamentally, the challenge of convincing others that your speech should be relayed. The internet is no different in that regard.