If the random characters are stored in the User ID field then 95% of the time the user just has to remember their password. It is only when the user switches to a new computer that they would need to type in the random characters. Wouldn't that be a significant benefit over having to type the random characters every time the user logs in?

I agree with your observation that "hey I had this really neat idea" is almost always an immediate precursor to making things worse. Almost.