>Many computer logins protect information other than the password-bearer's
That is my problem, as the user, not yours. If you'd like to help, then just put some warning or notification on the form, and I'll appreciate that. Just don't prohibit registration if password of my choice is eg. '1'.
Most of the time, your bussiness - is your service, not the access to it.
Many computer logins protect information other than the password-bearer's- for example, any business or government. As a result it's best to consider it, then discard as your use case may require.
I absolutely agree on the account recovery point - it WILL happen, your choice as designer is just whether it happens within a designed process or without.