Ideally they wouldn't care much about the day to day operations of a company or even that it is profitable and they would use their voting shares only to prevent decisions that actively cause societal harm or to favor ones that actively benefit society.

Like I said, there's still a lot that could go wrong with that scheme, but it isn't like the current scheme doesn't have its problems too.

How would you manage this very site by these criteria? Would you still cover cryptography, freedom of information, civil unrest and bills which damage fundamental rights?

Does this site even make money?

Ok, assuming that we're treating HN like a business and that business is large enough to have significant government voting share under this scheme:

The government voting with its shares to silence those stories would potentially be actual censorship under the US constitution, and therefore illegal. The same cannot be said about private owners.

Of course, the government could opt to transition the site away from those topics entirely, but again that's something the private owners could do too.

And none of this prevents small competitors from coming in to run those stories.

Let me turn it around: Would Facebook have more or less freedom of speech with government control?

I’d assume Facebook would be appointed a partisan czar during each administration, much like many government agencies. Unlike the EPA or FCC though, controlling Facebook has huge political implications.

Right, so it is best we leave that to Mark Zuckerberg, who surely has no political agenda whatsoever.