How and when to verify one's self seems like more of a philosophical discussion.
If you want chess.com to verify you, you'll need to be patient, as it seems they have no idea what they want the Verified program to become. At least none that they've let us know about yet.
No other information has been released on if the verification program will continue, be discontinued, or changed to something else. It's also not a beta related process.
The verified program could have been modeled after Twitter's $8 verified scheme. It failed on takeoff. Maybe thus the pullback by Chess.com.
Nothing has been posted about it since. The people that are verified are lucky!
Frankly, I don't know what Danny's problem is with the Verification program. As I can see, it's just a program where if people want to pay $15(ish) to have a tick, what's so wrong about that, to quote him, "Everyone loves a blue checkmark".
Also, this site gets more revenue, so not sure what the problem is.
I tried to ask him, and all I got back was 'he has seen' my DM on Twitter. Unfortunately, he doesn't reply to me now... 
Frankly, I don't know what Danny's problem is with the Verification program. As I can see, it's just a program where if people want to pay $15(ish) to have a tick, what's so wrong about that, to quote him, "Everyone loves a blue checkmark".
Also, this site gets more revenue, so not sure what the problem is.
I tried to ask him, and all I got back was 'he has seen' my DM on Twitter. Unfortunately, he doesn't reply to me now...
Part of it was that it didn't get the adoption expected. Apparently not enough to justify holding cash prize events for verified members a sustainable thing, not enough to make preferred pairings between verified members, etc.
A lot of people just thought it was a cash grab.
CCOK
Yes indeed
What happened was the Magnus vs Hans vs chesscom catastrophe.
Hans has a blue check: https://www.chess.com/member/hansontwitch
Which means he passed the verification process and its 'even more rigorous fair play review' and was 'thoroughly-vetted'. https://www.chess.com/news/view/announcing-chesscom-verified
He was going to play in the 2022 Chess.com Global Championship with all the other verified players.
Then Magnus ridiculously accused him of cheating over the board. Then chess.com took Magnus' side and revealed that they had banned him previously for online cheating, uninvited him to the CGC, and published an accusational dosier on him. And now they are being sued.
Hans' blue checkmark is a shining neon sign that chess.com %$#&@# up in someway, or possibly multiple ways. They have thoroughly embarrassed themselves with it. Not to mention possibly placing themselves in legal jeopardy with it.
It's a shame because in hypothesis it seems like it could maybe be a good idea. I certainly like the idea that hypothetically anyone anywhere in the world could end up competing with the world's top players in a tournament.
How long will this take? When can i verify myself?