So you just made the password a link. What's the difference? In the end, it's just like randomly generating the password for a user (which has been used quite a bit in the past - and most of the time, it meant that you simply kept the registration e-mail in your mailbox).
Clicking on a link isn't a free action - the user is passing some information from his e-mail interface to you. Sure, most of the time nowadays this only means a referral, but that's still a piece of information.
The main problem I see, however, is that you expect the user to click a link in an e-mail you send to him. Most people don't read the links - they just click them. So someone can easily send an e-mail to everyone registered on your site (the recipient has no way of knowing it's really you), and send them to whatever site they want - because you've taught your users that clicking on links in your e-mails is just fine and to be expected. And then you give them the option of YourAwesomeSite Toolbar! and they install it, because they trust you. Or you use a security bug in Flash or Java, whatever.
Remember, people are always the weakest link. They know they're supposed to treat their passwords as a secret. They don't know that anyone can send an e-mail that pretends it comes from you.
Oh, and from user experience point of view, this is just silly. I don't want to login to my e-mail and search for one specific message just to login to your site - that's a great way to simply stop using your site. You may think that it's fine to just keep the user logged in, but that's something I only do with very few sites - I tend to avoid persistent sessions (and saving passwords). And as for your Facebook example, indeed, I only open it in a separate browser and in an anonymous session - the same as with any other annoying tracking site. Consider if you had to login to Facebook by clicking an e-mail link - do you see the problem with that now?