and this requires devices to exchange the shared private key which is inherently risky.

There is some risk, sure. I don't see how this would be any more risky than a TLS exchange. Obviously the exchange can be implemented badly, but if done correctly it seems like it would work with certs and send the key encrypted.

I think the bigger risk is the key sitting at rest on multiple devices, some of which are easily lost (cell phones) and could then compromise an account.