Thank you, that is a great explanation.
I do get where Beehaw admins are coming from. They want their instance to be a tight-knit safespace, and it is pretty hard to accomplish when there are only several admins dealing with an insane wave of newcomers. Unless Lemmy moderation tools get better, that seems like an OK temporary solution. Though, it is still kinda unfortunate that federated services, while being a great idea overall, are so prone to balkanization (that is, essentially, the fragmentation of mastodon situation all over again) but it gives user choice.
I'd say that phone/face verification is an overkill. Moreover, as you have already mentioned not everyone would go for it. Especially the kind of people who like Fediverse and open-source software in general will be more wary of such practices in general, I suppose. I'm not a fan of such practices myself because I care about privacy and the proposed tactic really reminds me of mainstream social media.
I think that so far the verification system works just alright. Being verified by a small text while signing up works. Using the same pseudonym and contributing to the community with quality content and decent comment history to build yourself a positive reputation also does.