* Algorithm can't be changed/improved without changing all your passwords.
* Your master password can't be changed without changing all your passwords.
* You have to remember yourself at what sites you are already registered, and in case of critical bug, you would perhaps need to change password at some services (again remembering which ones they were).
With that said, I really like the outside-of-the-box thinking on this.
These issues are definitely solvable, at least if you use a hybrid concept: while most passwords are generated, some can be encrypted and stored (encryption key derived from the master password). Easy Passwords has this functionality and LessPass appears to be working on it as well. Then changing algorithm or master password can be done by converting all existing generated passwords into stored password. This isn't a great solution of course and so far I haven't seen the need to implement this escape hatch but it can be done if absolutely necessary.
As to remembering the websites where you registered - that should definitely be the job of the extension (not storing passwords doesn't mean that you cannot store metadata). And many password generators support a revision counter for passwords, you increase it when you need a new password.
I could not agree more with the points you mentioned. To solve the last one I added the option to create an encrypted list for the sites. But so you end with an additional password you need to remember because using the same as for the masterkey makes this the only key to access every password. And this is what the system tries to avoid.
If you compare this to two factor authentication it's the same amount of extra work, but without the benefits.
You should also avoid copying passwords to the clipboard as many applications and even web sites might have access to it.
Too bad client certifications are deprecated, now when SSL/TSL is becoming more and more popular. Only downside with client certificates is that you have to copy the key (witch can be password protected) to all your devices. Another downside was that the site required SSL/TSL, but almost every site have that now!
Personally I'd love to see UAF or SQRL take off. Lots of potential there.
As a work flow nit-pick, what if the password requirements change? You need to remember the original settings to generate your password, but if the site now says "must include numbers" when it didn't before...