A lot of that depends upon the government in question. Some want publicly funded news organizations at arms length. Others want to dismantle them. Some want at least the image of impartiality (and will take some criticism). Others want them to be a mouthpiece. It's not terribly different from the private sector. I would go as far as saying it is no different from the private sector given the consolidation of news organizations over the past few decades.

Why is that a problem?

> The problem for BBC is that it's government-funded.

That's not factually accurate. The BBC is principally funded through the licence fee (i.e. directly by the viewers).

It's inherently dependent on the government. The viewers don't get together and voluntarily decide to fund it.

Unfortunately I don't think there's a single such organisation in the world-- controlled-by-members newspaper. Even almost-controlled-by-members newspapers here in Sweden aren't fully subject to member control, with this typically being indirect through some board or similar organisation.

Guardian comes to mind.

The Guardian seems to be seeking money from the foundations of very rich people.

This is the precise opposite of what would be required.

> Guardian comes to mind.

The Guardian's ownership is independent

The Guardian's views are very much not. Very predictable