Why do you need it? Because you don't want to implement a login system? Very, very few websites are the sort of place where they'd want to authenticate with only a Bitcoin address. If for no other reason than they'd have no way to email you, and if you lost your wallet, you'd lose all your associated data.

Well, the major difference is that you could sign up effortlessy to a service, and associate your email later.
If more people sign up to more services, it's a good thing for the ecosystem.
 
 
Without such a standard protocol, you could never envision a pure Bitcoin physical locker rental, or booking an hotel room via Bitcoin and opening the door through the paying address.

In future there often won't be a simple paying address. For instance, if my coins are in a multi-sig relationship with a risk analysis service, there will be two keys for each input and an arbitrary number of inputs. So does that mean the risk analysis service gets to open my locker? Why?
 
What if I do a shared spend/CoinJoin type tx? Now anyone who took part in the shared tx with me can get into my hotel room too?



In a perfect world, you would pay your locker with a "normal" transaction.
The same way you shouldn't play satoshi dice from a shared wallet.

But your point is totaly valid, and I don't have answer to that except that I'd love to have a Bitcoin authenticated locker in our Bitcoin co working office.
 


These are the kinds of problems that crop up when you mix together two different things: the act of paying, and the act of identifying yourself. You're assuming that replacing a password people can remember with a physical token (their phone) which can be stolen or lost, would be seen as an upgrade. Given a choice between two physical lockers, one of which lets me open it with a password and one of which insists on a cryptographic token, I'm going to go for the former because the chances of me losing my phone is much higher than me forgetting my password.

All the tools you need already exist in the form of client certificates, with the advantage that web servers and web browsers already support them. The biggest pain point with them is backup and cross-device sync, which of course wallets suffer from too!


Bitcoin users are normaly already paying some effort to securise and backup their wallets / keys. So it's just about leveraging that.

I would myself pick a crypto locker, because I'm the kind of guy who Facebook connects and I follow the easiest path, even if it has long term costs :)

Eric