That would require the user to be quite vigilante when they are entering a password on a website. Getting up to go to the bathroom could mean someone steals their password.
"Of course, my preferred solution to this problem is to allow the user to toggle the password field, so that they can view the unobscured text if they wish"
I am assuming that if the password field is being toggled, that it is not actually a password field but rather a regular text field with some javascript stuff messing around to hide the text. That would probably function just like a username field. I'm not really a web developer though, so it is possible my analysis isn't correct.