They weren't "private" TV networks. They are licensed by the government to use our airwaves, which are accessible by all (except CNN, which is cable).

There's a big difference.

Governmental and public institutions should not be relying on Twitter for their communications. It's unprofessional at the very least.

They absolutely were/are private, even if they used a publicly owned medium to distribute their content. Other than an hour of public-service airtime on Sunday mornings, and lax FCC enforcement of a decency standard, those private TV networks can do/say anything they want.

You wouldn't put quotes around that word for cell-phone companies using licensed bandwidth, or airlines using public airspace, would you?

The broadcast companies are subject to FCC requirements that they must broadcast government emergency notifications. They do NOT have the power to shut down access the way twitter just did.

I might. It depends on what you're talking about, especially airspace. Witness Musk's tantrum over the public nature of airspace usage: https://www.protocol.com/elon-musk-flight-tracker

And they are not private. The public is legally entitled to receive anything broadcast over the radio spectrum. And as I and another poster have already pointed out, there are government licensing and carriage requirements involved with TV and radio broadcasters.

I don’t have an issue with governments using “private” cell phone networks for amber alerts, if that’s what you’re asking

I keep hoping that in the near future we will think of companies/NGOs/influencers/Governmental Institution on twitter as using aol.com for their email.