The list of usernames is public, so it would be useful to do client-side validation of usernames on the password reset screen.
It is not public which emails are in use, so we should not reveal that in any way (the current password reset interface does not either).
T42040: Special:PasswordReset could use some design love
T19544: Client-side validation of the username availability (done) and that password meets requirements
T36447: "Check Availability" feature for usernames at registration interface
T49685: Add password and username checking JS to core login and signup forms