The argument seems to be that consistency allows you to prove ownership and re-use all of your content etc across the web by tying everything back to one verified identity. If you are having different identities on different sites then that benefit disappears, and I fail to see how it is then any better than using email addresses? You end up with different wallet IDs each with their own island of content, just like you have with email addresses.
Sure you could chose to "move" content with one of your many identities by just logging in with the ID (presumably losing all of your existing content), but we have copy-paste for that already (and I am only half-joking saying that...)