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The spoofing site could just pretend your U2F was valid and get your password, although it couldn't really do anything with it anyway.

The spoofing site wouldn't/shouldn't be able to pass the browser validation of the TLS server side certificate.

Why not? How hard is it to get a cert for a domain that looks like paypal-businesscenter.com?

Moreover, the browser could remember the expected shared secret based on its and the server's RSA exchange.