Without getting into "could, would, might, should" arguments I'll just point out that the current crop of TESLA HPWC (and other manufacturers) do communicate via WiFi and the Tesla ones also communicate with the car via a separate RF link. Why would they limit themselves to J1772? They want, of course, to be able to have their cars charge from any EVSE that meets J1772 and so are capable of that but they don't limit themselves to what J1772 covers.Since there is no provision in the J1772 standard for the vehicle to communicate anything with the EVSE, it would require reworking the standard. It could be done - in theory - but in practice it is unlikely to happen.
And we also need to take note that J1772 is being reworked. The newer standard calls for much broader communication capabilities.