Sounds like a tracking nightmare, right off the bat. There is absolutely no way this will not be used for tracking.
Each session is backed by a unique key and DBSC does not enable sites to correlate keys from different sessions on the same device, to ensure there's no persistent user tracking added. The user can delete the created keys at any time by deleting site data in Chrome settings. The out-of-band refresh of short-term cookies is only performed if a user is actively using the session (e.g. browsing the website).
DBSC doesn’t leak any meaningful information about the device beyond the fact that the browser thinks it can offer some type of secure storage. The only information sent to the server is the per-session public key which the server uses to certify proof of key possession later.
All nice and dandy, but what constitutes a session? If you want people to stay logged in after killing the browser, that has to be stored somewhere.
I have absolutely no faith in this. And if there's malware that has the same rights as the browser, how will the TPM help? This is a serious question. How will the TPM help?