Since virtually every service has a 'forgot password' option, all the OP is suggesting is to formalize this as a default login process for second tier services

Since virtually every service has a 'forgot password' option, all the OP is suggesting is to formalize this as a default login process for second tier services that are too much of a bother to keep track of. The net positive, if this were implemented across the board, is that users would focus their efforts on securing a few high value accounts, versus reusing the same password across dozens of low value accounts (chain, meet weakest link).