And this is really just being considered from the perspective of what Twitter being sold to users means for Twitter shareholders. What about what that means for Twitter's users? Will using Twitter require having to purchase a share of stock on a public exchange? I think it's a pretty bad idea all-around. Unless they're incredibly smart about this (not even sure it's possible to figure out), all of a sudden dilution of Twitter stock is linked with adoption, and voting rights are linked with number of Twitter accounts, and having a Twitter account is linked with ability to purchase stock which is not exactly an anonymous, private thing.
Credit unions have a decent handle on customers-as-owners, so it's not completely without precedent from a business standpoint.
My biggest issue is your last point, where owning an account would likely involve "Know Your Customer" levels of identity proving. It would likely require a new class of shares or going private, rather than buying a share on an exchange. Similarly, you'd likely only get one share no matter the number of accounts (using KYC information to de-dup, or having two notions a "member" who can have multiple "personas").
I don't know that it's a good idea for Twitter, but it's at least a (sort of) legally workable idea for an authenticated messaging platform in the abstract.
If I were starting a new Twitter, I'd consider it.
