I highly doubt the typical user with password "1234" is going to go through the trouble of using this service. They would most likely email the password directly ("that's secure right?")
You know what's funny? The company that I work for wrote a web app for a large company and we also host it for them. At one point in time, they requested a way for users to reset their passwords. We implemented it, but they never use it. They prefer to email me their passwords in plain-text. I think I've handled two of these types of emails today, alone!
"I'm sorry, but we recently reviewed our security practices, and we've found this method of communicating passwords to be incompatible with our dedication to protecting the confidentiality and integrity of your business data. Please use the the password reset form at .. "
