That is a very good point to which I have no counter-argument. In fact, if we look at BBC as an example, they’re publicly funded and maintain high credibility and a high degree of press freedom.
while i haven’t looked into it particularly, i’m also sure there are ways to de facto public-fund media while still creating separation from the state if you’re really worried about that. like, there probably isn’t just the single way to publicly fund media and you have to either accept that model or not publicly fund media, right?