I think the best way to look at things is to look at platforms that don't and have really never had issues with verification to begin with. An oddly good example is YouTube, which has a verification feature that's so uneventful and drama-free I reckon a lot of people hardly even notice it. Even fairly small scale musicians and creators, at least relatively speaking, can have verification symbols. (Of course, there can be issues with e.g. account takeovers and people changing their name/icon to try to fool you, but that's not really a problem with the verification process itself.)

The trouble with what platforms like Twitter did was by trying to stick to some definition of important, they took what should be a mundane "yep, this is the person it looks like" icon and made it into a status symbol that everyone wanted. Twitter had a hard time defining the boundaries: Shouldn't they verify their most influential users even if they're not real world celebrities or public figures? What happens if someone who is verified says something that they don't like? How do you prevent corruption when you give other organizations special privileges for verification?

For Twitter and Instagram verification, people were bribing employees and getting verification just because they joined an organization (like an eSports team or a news organization.) This was not a good status quo.

Bluesky is probably headed towards the same problem if they try to be the bearer of who's important. Obviously, you can't verify any Joe Schmoe, but honestly you can just set a reasonable threshold based on their status in the platform for as to whether or not they should be eligible to get verification. When you do stuff like say "You should be able to be verified because you work for NYT", that's just weird. Being a journalist doesn't magically make you important, or mean that your posts will be worthy of greater consideration, yet that's what you're setting people up for when you make verification into a big ordeal like this, and it's the reason why Twitter would unverify people for e.g. having an opinion too far outside the Overton window. And using in-platform metrics to determine eligibility seems reasonable anyways... If you have like 10 followers, your verification status is utterly meaningless anyways.

I think if they want to solve the problem for journalists they should've verified the organizations and then made this separate from verifying individuals. Then accounts under that domain could just have some sort of special badge. This especially makes sense because otherwise you could literally just have your personal account become verified by having a couple month stint at the NYT or something, which is non-sensical.