The COSE draft also refers to "OKP" keys: https://tools.ietf.org/html/draft-ietf-cose-msg-24 which in my opinion speaks for separating the CFRG algorithms from EC.
OKP keys have as far as I can tell (I'm not a cryptographer, just an applier of cryptography), no ECPoint, coFactor, and ECField and an entirely different ASN.1 representation compared to P-256 et al. WDYT? Anders Just updated: https://github.com/bcgit/bc-java/issues/193#issuecomment-309183825
