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Only someone with my Trezor could create a valid signature. It allows a lot of cool uses where no one can pretend to be you without the actual hardware!
Ummm.. yes. That's the problem, exactly.
Passwords, 2-factor auth, could all be a thing in the past! The Trezor keeps the private key hidden and secure. As long as I keep the device safe, my identity is safe. And for the online world that is a VERY exciting thing!
... that's basically advocating a return to 1-factor verification (using a Trezor instead of a password). There may be a lot of great uses for a Trezor but that's not going to be one of them!
Don't get me wrong - the Trezor is a great innovation for bitcoin, with many other potential applications, but hardware signing has been tested, used and mostly abandoned for online banking over the past two decades (crypto-boxes, smartcards, etc.). Just saving you some time.