If there is anything on the web more annoying than having to log in, submit a captcha, copy a message for two-factor authentication, answer an email, then log in again, I have yet to see it.
My idea is to provide hardware-based logins for web sites, allowing you to log into your device and then never having to type in a password for as long as you're logged on to the device. This could be implemented by using something like a YubiKey or some other device that generates a random certificate that gets put on the device and submitted in place of a password for any Mozilla-based login. From then on, the website then checks this random cert instead of asking for a password.