If/when users do as Flickr is asking, I wonder if Yahoo will redirect them to use Yahoo Mail etc. In any case, I'm not a flickr user anymore but it would be interesting to know how smooth they've made this process.
My biggest issue with Flickr is that they tie it to a @yahoo.com email address. I know it's part of the "ecosystem", but c'mon—who uses one of those?
When you say "this", what are you referring to?
I can see not wanting one company to always know when you're logging into other companies (hence the lure of Persona), but this particular situation (you can no longer use third-party authentication after eight years or whatever and must now use first-party authentication) doesn't seem like a reason at all.
It is the top comment and having a username+password option is still reassuring even if you choose to go with facebook or another third party anyway. Many will only use facebook to login if there are alternatives.