I enjoy the way you think and phrase your thoughts (are you on ketamine?), but I think that publicly-owned broadcasting, particularly (exclusively) the entertainment side of things, is the opposite of republic misdesign. it's a freak accident of something very very positive and joyful and broadly selfless rising above the waves of self-interest and corruption and misery.

I think the news part of the BBC should be removed, maybe spun off into a separate entity

I think you misunderstood my sub-point.. I think we both agree about the BBC as a wonderful result. I question the motives for a special system of protecting it in a government that doesn't seem to get any better at other sectors.

Of of the BBCs jobs is to scrutinise the government. Editorial independence is essential. You can argue how well it does this, but if the government has direct control over its funding, it clearly won't be doing that task any better.

my understanding of the justification for a special system is that it's inherently more fragile and more tempting to attack than other government services, which generally provide tangibly vital, life-preserving services, rather than less tangible artistic and cultural ones, and the particular form of the service lends itself to being funded in a way that wouldn't work for other more vital services

healthcare is possibly one of the few that could (i.e. does in other Western countries) work similarly, but people including me would undoubtedly despise it. most things need some kind of mandated funding otherwise they would fail and people would die, go homeless, not have a military or live tangibly worse lives, and mandated taxed funding is generally better because it relies more on those with broader shoulders

overall I personally reject your notion that there's some kind of subversive justification for it