When I went to Settings > Messages and tried to de-select my email address from Send & Receive, it wouldn't let me. I then noticed at the top of the screen that even though iMessage was "on", in small print beneath iMessage it read something to the effect that iMessage did not authenticate and to try again. I turned iMessage "off" and then back "on" again and the authentication started over and was successful. My text messages now show that they're coming from my cell phone number and now my cell number is "checked" as the option under the Send & Receive > Start New Conversations From.
BTW, I still can't seem to delete my email as an option, but since it's no longer showing as where my messages are coming from, it's not a problem. Having the email address associated with your AppleID is probably a default/fallback setting Apple has established which makes sense.