Passwords are unsafe for the same reason that roads are unsafe: human beings. Things work well enough for most people, most of the time. However, during certain situations, most people aren't trained correctly and often do the wrong thing. What's more, there's even an accepted culture of doing the wrong thing.
It still doesn't prevent users from being stupid w.r.t. writing down passwords, but it at least presents users with reasonably secure logins that are relatively easy to remember.
And by plain-text, I mean the server receives information that could then be used to authenticate later.
For instance, if you send the sha of a password, and then store the sha of the sha, you're still sending the password in plaintext, it's just that it's not the password the user entered.
This method is no less secure than the standard "client sends server password over HTTPS" scheme.
... and how do you set up a secure connection without a pre-existing password?
Your solution has a chicken-and-egg problem.
SRP does.
[0] http://en.wikipedia.org/wiki/Secure_Remote_Password_protocol
[0] http://en.wikipedia.org/wiki/Secure_Remote_Password_protocol
https://www.lightbluetouchpaper.org/2012/05/22/the-quest-to-...
They fail when their correct use depends on human beings. Just like you said.