The marginal cost of verification could be zero. All Twitter has to do is to get together with Facebook, Google et al and agree to support a number of approved independent identity systems such as Yoti [1]. That uses a combination of government documents (eg passports) and biometrics.
Basically, users would be able to sign up for a sort of "digital passport" ID that would, in the long term, be accepted by governments and most websites. Enough people might find it convenient enough to sign up.
Twitter already allows you to block all users who have not registered a phone number and not uploaded a photo or whatever. I used these settings. They actually do remove a lot of bots and bad players. Again, in the long term, Twitter would give people the option to see only verified accounts.
I really wouldn't care if it meant I only saw tweets from a relatively small number of verified accounts. It might be more like Twitter in its first half dozen years, when it was much more engaging and fun than it is today.
Not exactly sure which method they'd use but seems like if they wanted to do it, they could put a lot more effort into figuring it out. I mean, Bumble, a dating app, does a simple (maybe too-easy-to-game) verification, but with so many banks having to abide by know your customer (KYC) requirements, then I think social networks could figure it out.
I don't know if Nextdoor's method of mailing a card to someone's mailbox would work for Twitter, but I like your example of a social network that has taken verification much more seriously.
In this way, as verified accounts increase, the unverified accounts become more obvious and I imagine we will start to view them with more scrutiny.
It would allow anonymity to remain, just make it so those accounts are more obviously anonymous or pseudonymous.