2FA basically ensures security via a second channel, and it's perfectly possible to store passwords in a secure format. I'm not convinced your ideas there are worth the cost.
Why? Almost all websites require email confirmation; sending someone a login-URL via email actually has less friction because the password-choosing step is removed!
> it's perfectly possible to store passwords in a secure format
But it's very hard to do so. Even if you use scrypt, it is very hard to make sure your whole system is actually secure against password leakage.
The simple truth is that letting your users choose their own passwords is a liability; and I've decided to avoid this liability.