That's not possible. If you use the internet a little bit, you are almost constantly required to chose more and more new passwords. To newspapers sites to comment, to registration forms, to buy tickets to some concert, etc etc. You cannot use different password for each of them. And password systems are overkill for most people (certainly is for me).
Really, what IS sensible is having sensitive sites with different passwords and "who cares" sites with simillar ones. As the author actally says in the end of the article.
Sure it's possible. Use a mentally computable one-way "hash" when creating your passwords, such that you (and only you) can generate a unique password based on some attribute of the system you're creating the password for (name, domain name, etc).
Of course that's also too much work for the average user.
I think single sign-on systems with two factor authentication and other advanced security are a step in the right direction.
Really, what IS sensible is having sensitive sites with different passwords and "who cares" sites with simillar ones. As the author actally says in the end of the article.