[inglor_cz]

The distinction between private and public sphere is not completely clear.

Let us say that a politician calls Mark Zuckerberg and asks him nicely to squish certain people, and MZ complies. Is that a First Amendment issue or not?

Or, let us say that a politician calls Mark Zuckerberg and offers him some concrete support (in an anti-trust case or taxation matters) for squishing certain people, and MZ takes up the offer. Is that a First Amendment issue or not?

The trouble with both scenarios is that they are certainly possible and hard to prove or disprove. That is one of the reasons why concentration of power in a few hands (even private ones) may translate into bad politics.

[munificent]

I agree with everything you say, but I don't see that "free speech" needs to be the hammer you use to drive in that nail. Concentration of power in the few is bad for many many reasons independent of free speech.