I think the current public/private key systems have many parallels with encryption/decryption functions.
For example, the generator point (which relies on the underlying curve) is the shared key, upon which all private keys are calculated with - in order to compute/derive the corresponding public keys (not including hashing/pre-address formatting).
So if one wanted to encrypt some plain-text message of a length less than the length of the key, it could easily be done with the private key as the one-time pad (OTP) to xor a message for example, and then at some point in the future decrypt that same ciphertext message by xor'ing it again with the original private key (then discard that address/key-pair, as the OTP shouldn't be reused). [Just to be clear I am not implying this is how private keys should be used from a public/private key-pair, but just pointing out that a private key "could" be used to encrypt, and not just to "sign" to prove ownership.]
However, to send that ciphertext to someone else, would require their knowledge of the original private key if they wanted to decrypt it. For longer messages, some key stretching function could also work for keys that aren't long enough, although caution would be needed that the method doesn't leak anything information about the key.