The problem you proposed strikes me as primarily being that one company controls the Internet. That's the problem that needs to be addressed. It might have implications for the speech issue you're suggesting, but I can safely punt on that. Break up the single monopoly in order to reduce the degree to which any one private actor acts as a pseudo-state.
A counter-example for you is the following: suppose that a million companies control the internet, and all of them independently decide they don't want to publish white supremacist content. Then the problem is clearly not concentration or monopoly or collusion, but rather companies (via the people who make publishing decisions for the companies) exercising their own free speech. I think the challenge is that in this counter-example, the free speech absolutist -- not saying you are one -- needs to admit that they want to restrain one sort of speech (not wanting to publish white supremacist content) to enable another sort of speech (people publishing white supremacist content). It's an essential tension. Someone has to lose in that exchange. We need only clarify who.
It may be the case that the internet is far closer to your example than mine, though I doubt it. Even if market share of social media suggests concentration, it seems to me easier than ever to publish your content. I published my first website in 1995 and surely I have an easier time doing it today than then. Now, I might not have an easier time getting an audience, but I am also not entitled to an audience. If people don't look for me or tune me out, that's not a violation of my rights. That the public has chosen to waste less time seeking out dissenting views is maybe something we should be worried about, but probably not something we solve by legislatively privileging access of dissenting views, no matter how nuts, to platforms.
I just wanted to add one final thing. Matthew Lyon was a congressman. When John Adams passed the Alien and Sedition Acts, Lyon attempted to publish a piece calling Adams a dictator and a tyrant for doing so. The local newspaper, the Rutland Herald, would not publish it. So Lyon started his own newspaper. Lyon was subsequently convicted and jailed. In this example, we see three things: (1) the government jailing Lyon is a restraint on free speech and unconstitutional. (2) The Herald not publishing his letter is not a restraint on free speech. (3) Lyon did what we would expect people to do: work to amplify their own voice when others will not.
Today it is easier than ever to "start your own newspaper". You might find that no one reads it -- but you are not entitled to their readership, just as Lyon was not.