TOTP is phishable. U2F isn't. It wouldn't be good for the world if TOTP became universal, as phishing would adapt. However, the single TOTP hardware device for

TOTP is phishable. U2F isn't. It wouldn't be good for the world if TOTP became universal, as phishing would adapt. However, the single TOTP hardware device for multiple sites that you postulate converges on the U2F design if you wrap the OTP in signatures so both sides know who they're talking to.