I would much rather see users have one master login on Facebook or Google with a long, unique password and behind two factor authentication – because lots of sites with mostly reused, simple 8 - 12 character passwords, all of them using weak hashes and just waiting to have their user database downloaded and hash cracked someday en masse is far, far more dangerous!
(There is really no difference between using Lastpass or whatever and Google as your single source of auth. If someone cracks your Lastpass password you are just as hosed.)
I also trust Facebook and Google a lot more than other random websites, even banking ones…