And they shouldn't. News should not be determined by its shareholders. The idea that such privileges should be able to be purchased is so incomprehensibly stupid, I'm at a loss for words.
It's obvious when the Washington Post writes articles about Amazon that there's a conflict of interest. They definitely write them, but I don't remember anyone sharing any stories from them about e.g. the HQ2 process. People know to look elsewhere. And conversely, the moment the Post publishes a news (not opinion) article about how every city should want to be HQ2, or worse, mentions it off-hand in an article about something else, everyone knows not to trust that and possibly to lose trust in the news source in general. So they don't.
It's not obvious when ownership is a thousand pseudonymous private keys when there's a conflict of interest. If a random article about a random company looks a little more negative than it should be, who knows if the current pseudonymous owners are shorting that company?
Publicly-disclosed ownership of the media by the rich has a ton of disadvantages, yes. But I don't the blockchain solving any of those disadvantages, and I see it introducing a new one that is specifically avoided by publicly-disclosed ownership by the rich.
How many people are actually informed that the Washington Post is owned by Jeff Bezos? How many people know that Jeff Bezos has contracts with the CIA[1] & sits on a pentagon board[2]? I doubt many. It's one of the few "left" wing newspapers I refuse to read for the reasons above.
I'm not arguing for this blockchain solution, I think it makes things worse exactly as you said.
Every time the Washington Post mentions Bezos, or a company he owns, even in the abstract (for instance, in this spaceflight article, which mentions blue origin: https://www.washingtonpost.com/news/business/wp/2018/06/15/f... ), they say that Jeff Bezos owns the washington post, in those exact words.
Given that the President of the United States went on a yelling spree recently about Bezos' ownership, I'd say most people who can distinguish the Washington Post from the Washington Times (owned by Sun Myung Moon's religion and absurdly right-wing) also know who owns the Post.
(Which isn't to say everyone knows that either—a lot of people seem to take the Times equally seriously—but solving the problem of bad-faith media existing is another one entirely, and quite probably the answer is it shouldn't be solved at all.)