OK I take it back, privacy is one of their specified goals:
> Note that the certificate chain for the TPM is never sent to the server. This would allow very precise device fingerprinting, contrary to our privacy goals. Servers will only be able to confirm that the browser still has access to the corresponding private key.
However I still wonder why they don't have TLS try and always create a client certificate per endpoint to proactively register on the server side? Seems like this would accomplish a similar goal?