Excellent idea. Might also help against the bot issues. If we could just turn off the visibility of non-verified accounts (or better still, make that the default) it seems misinformation would be a bit harder to spread.
For me, at the moment, I'm genuinely concerned about the rise of bots and their impact on online discourse. I'd love to see measures put in place to flag or prevent their use. You only have to look at some of the comments on a Trump/thunberg/Sanders post.
Or integrating https://botometer.iuni.iu.edu/#!/ Intro Twitters service or building their own _and turning it on my default_
Certainly doesn't have to be the verified account direction, but, something needs to be done.
I'm all for identity verification and having a strong online identity (e.g. I really like Keybase and Estonian PKI), but being identified shouldn't mean one can be trusted.