The point of accepting OpenID is that then people aren't limited to the few huge-name organisations you accept. Many of us don't want to log in with a Facebook, Twitter, Google etc. account precisely because those organisations don't allow us proper control over our identity.
An OpenID, on the other hand, can be had from organisations much more friendly to their users, or can even be provided by the person individually if they choose. Please let us manage our identities with the standard for doing that: OpenID.