Austria tried that by forcing citizens to pay for the state media directly instead of tax money, but it pretty much failed because politicians just can’t get their hands off that and so always place their own henchmen into management positions there. Obviously they’re also unwilling to create laws to get rid of that power.

NPR & BBC are probably the closest we've got so far - they're both state funded, but editorially independent (theoretically). There's still some influence from the government, but it works pretty well.

Edit: public-funded news outlets definitely work best when they're part of a larger system including other models of governance (like independent non-profits) as well.