What is the benefit of using ONLY OpenID authentication on a site?

The benefit of making OpenID mandatory is simply that login code for the website does not need to be written (beyond the OpenID integration), and no precautions need to be taken around storing user passwords etc.

Not having your own login code also means not having to deal with a lot of support issues like resetting of lost passwords etc.

Certainly most of your downsides are valid, so I guess it becomes a trade off.

What surprises me is that there are not more sites forming a close relationship with a particular OpenID provider to simply the account signup phase - i.e. some sort of 'You can use any OpenID you like, but you can also create one right now by entering a username and password etc' login page, which automatically creates a new account with the selected provider for you.

It's a good way to outsource a part of your infrastructure. You don't have to worry about lost passwords etc., someone else does it for you.

I'm not sure I'd use it exclusively, though. I haven't used OpenID enough to entirely trust it, and the sign up process needs to be streamlined until > 90% of users have an OpenID.