I think this depends entirely on the context of the website, if for example you were building an e-commerce system and you wanted to streamline the sign up process so you can start building up analytics on that user as quickly as possible from a variety of cross platform devices that they access then an email address would suffice with a auto generated password.
Remember at this stage the user has no personal details stored within their account, they have only entered in their email address, and perhaps a name? The auto generated password / email would then force the user upon next sign in to change their password, you can hardcode the password into the link itself.
No information at this point could be considered to be 'dangerous' if it got into the wrong hands, and at this point the user is changing the password to one they feel safe and secure with.
However if at the sign in screen you are taking address, phone number, card details then auto-generating a password would un-secure and pointless, the user has already entered in a myriad of data, what would one / two extra fields be?
Would auto generated passwords work for banking, car loans or other financial services? No, for websites / accounts that have no personal information that could be used, yes.