All journalism becomes volunteer work, running off of optional donations, which seems unlikely :D
It’s not quite that simple with PBS or NPR, but that’s the basic idea. Open public funding with no political or corporate control sounds like the safest bet. It’s as viable as people deciding to support it.
Not sure why you’d think “publicly funded” would seem like the “optimal” option. Same thing structurally as “state-run media”, just friendlier phrasing. If we had direct democracy or something, that might be fine, but the fact that it has to run through politicians and bureaucrats with their own interests/agendas, that completely changes the picture. If you have that federally funded in the U.S., that basically just tucks under the executive branch like almost everything else, meaning it’s just managed by the President, with basically only a paper tiger of regulations preventing interference in place.