A Note
I have a very good understanding of sessions and the theory of secure web-based authentication, etc., so please don't start with the basics, or give ambiguous answers. I am not looking for Best Practices, because I am aware of them. I am looking for the real risks behind them, that make the Best Practices what they are.
I have read, and agree with the principals that nothing more than a Session identifier should be stored in a Cookie at any given time.
The Story
However... I've inherited a rusty old app that stores the Username, Password, and an additional ID, in a Cookie, which is checked throughout the site as verification/authorization.
This site is always (can only be) accessed via HTTPS, and depending on your stance, is a "low-risk" website.
The application, in its current state, cannot be re-written in such a way as to handle Sessions - to properly implement such a thing would require, essentially, re-writing the entire application.
The Question
When suggesting to the-powers-that-be that storing their user's IDs/Passwords in plaintext, in a Cookie, is an extremely bad idea, what real risks are involved, considering the connection is always initiated and manipulated via HTTPS?
For example: is the only obvious way to compromise this information via Physical Access to the machine containing the Cookie? What other real risks exist?