It’s not to verify identity. It’s more like imprimatur (anointed by Twitter as whatever). And that is stupid because it’s basically up to the whims of the company and becomes open to abuse internally and externally.
Unfortunately, there's a strong correlation between "useful to verify" and "important", so pretty quickly it became a status symbol, especially for marginally notable people. And some people really like status! It's very similar to the problem Wikipedia has, where they daily have to delete a lot of BS biographies from the would-be famous.
This means that the program has been a headache for Twitter for a long time. I know when I worked there in 2017 they announced that they were suspending the program pending a major revamp of how it works. As far as I know nothing came of that; I think they quietly started giving out blue checkmarks again a while back.
Personally, what I'd like to happen is that they make it much broader and roll it up in a "Premium Twitter" feature. I pay them $50/year, they verify that I'm who I say I am, get rid of ads, and throw in a few other features. But I doubt that will happen, as IMHO Twitter is incredibly bad at getting anything done.
There are some groups that take it as a warning sign for craziness. Funnily, it often seems they are onto something.
I think that is precisely the purpose. If you’re looking for Donald Trump’s Twitter profile the idea is the blue tick helps you find the right one rather than a parody.
IMHO these were pretty clear anti-abuse actions. But of course those people claim that they were being punished for their views.
I don’t know how true that rings.
For example both Sanders and Trump have a blue tick. They obviously can’t simultaneously be representative of a majority of Twitter’s staff’s views, can they? And I’d estimate Trump isn’t representative of a substantial number of these west-coast tech workers at all. So that doesn’t seem to hold up.
Assange is an interesting case in that despite renown and following they refuse to give him a check mark and suspended the WL account as well.
PS I tweaked my comment after you started to write your reply but before I saw it; the wording is better now but the meaning is basically the same. Sorry!