However, from the point of view of someone implementing an authentication system, passwords on their own are broken. There will be a significant fraction of users who re-use their password at a site with minimal-effort security. If you subscribe to the idea that computer professionals have a moral duty to safeguard people's private information entrusted to them, then password-only authentication is just broken.
The solution is to either: spend the money to implement a multiple factor authentication system (with a secure password database and fraud detection) or use a federated identity service. (Even just sending a one-time login code via email is fine). The latter is simple and takes even less effort than implementing a password system from scratch.
There should be fines (at the very least) for having an unsalted password database with more than X number of users.