I agree with you that a technical solution is needed. Forcing developers to store passwords securely, experience shows it doesn't work. But how exactly would your solution work? If I work at a computer I haven't used previously, how am I supposed to authenticate to a site without using a password?
The first step in the SRP protocol is to retrieve the cryptographic salt from the server, so you're essentially free to roam.
This step has concerns of its own though... for one thing the request itself reveals that the username/id is valid, and if you cache the userid / salt pair on the client machine it's vulnerable to snooping by other people with physical access. There are some fairly straightforward tweaks that can be made to the protocol to work around these issues though, since the salt isn't sensitive. In fact, I'm pretty confident storing the salt server side can be eliminated.
I think the idea is that the browser would implement SRP. That means you would still type a password into your browser, but it wouldn't be sent to the server. Instead, the browser and server would authenticate you by means of exchanging specially-designed hash codes.