So if noone else is going to make a coherent argument for it, I'll play devil's advocate here.
The purpose of a government is to protect the rights of its citizens. That's my view, anyways.
So education, healthcare, infrastructure, legal system, defense, emergency services etc. - all crucial services that a government should provide through tax and spending.
But TV, film and radio? As a form of cultural education.....yes, probably. I can see the argument. But UK taxpayers (let's be honest - the license fee is a tax) already pay between £3.5-4 billion a year to cover this through the BBC.
The rationale behind the creation of Channel 4 (by Thatcher of all people!) as a complement to the Beeb was to provide a combination of quality and diversity of programming. And in the 1980s, that was clearly necessary. When you only have three channels, bringing in a fourth makes a big difference in terms of viewing choices and options.
But in 2022? Hard to argue that viewers don't have quality, choice and diversity. I'll admit to not being 100% sure what TV and streaming services are available nowadays back home, but I believe there's, what, about 50 channels now available on DTT and then presumably it's some combination of Netflix, Amazon, Apple, Disney, HBO and some smaller streamers? There's a massive range of programming available across those channels and services. You'd be having to look in some pretty tiny niches to not find anything you want to watch across them all.
So I struggle to see how a logical argument can be made that the UK government needs to own Channel 4 to protect any rights of UK citizens.
The only argument I'm hearing is the legacy argument - it's always been this way, and it's not doing any harm, so why change it? Which is always a weak one, in my opinion, if there's no real guiding principle behind it.
I don't think I would be approaching privatization in the same way i.e. flogging it for a billion to the highest bidder.
I'd probably first be going to Channel 4's current Board and management and saying "Look, we don't want to acting as your guarantor as a statutory corporation any more, but we're happy to hand this over to you to run as a 'Company limited by guarantee' (or whatever is the appropriate not-for-profit company structure)". See if there's interest in continuing to run it as a mission-based organization before juest auctioning it off.
But ultimately, I just don't think I see the moral argument for why Channel 4 should be state owned. The model for TV has profoundly changed in the past decade, so ownership should probably change with it.