What if you use the email as extra bits of entropy? Like you can append the password to email then hash it. Of course you lose the ability to send emails and account recovery, but its an okay tradeoff for people who want more security.
Recover password by email is a business requirement. You also need to be able to send users an email to alert them about numerous things such as credit card expiry or service termination, etc. It sounds like an option, but I don't think it's an option any real company will take.