I'd be on board. Anonymous users would stay anonymous; users that are comfortable confirming their identity would get a blue badge. I don't see a downside, and I see plenty of upsides.
I wouldn't go as far as to require government ID, (some folks have issues getting government IDs for voting purposes) and many undeveloped nations have large portions of their populations that have no birth certificates.
I would however require that a human be present to create a new account and that it be tied to a phone number for 2FA or something along these lines that makes mass registration cost prohibitive.
What if there isn't a lot demographic overlap? Twitter doesn't provide any kind of tooling that would allow one to follow only the relevant tweets in a given account. This is especially relevant if the interests/communities at issue not only don't have a lot in common, but actually spend a lot of time at odds, which is the case for many interests. It'd be impossible to have some followers from such groups who wanted to hear about the one thing without simultaneously alienating them by talking about the other thing. Computing and hunting are good examples because your average cypherpunk's opinion and worldview is much different from your average hunter's opinion and worldview.
I have personally started a handful of different Twitter accounts intended to engage with different communities. None of these perform any automatic activity at all and I basically use them for a couple of days and then give up because it's too much effort (recently, more because Twitter blocks the accounts almost-immediately).
More accounts than people is absolutely not a reliable indicator that "you have robots registering" (especially when businesses etc. are expected to register). That may be a better metric if Twitter provided useful filtration tools, but even then it'd be shoddy.
And you should be able to filter out posts accordingly, like "only showed verified" or "don't show suspected bots".
And by default, Twitter should hide suspected bots in reply/hashtag threads, so they don't get increased exposure.