After much foot dragging, and vastly underestimating the numbers affected... (ISTR was something like 160+ million in the end including a significant number in the UK).
Having Experian, come along and let you know that they have just handed copious quantities of sensitive information to potential fraudsters, does not do much to mitigate the damage. (They did offer a years free access to their ID theft monitoring service - presumably reverting to paid after that - so basically treating their c*ck-up as a marketing opportunity!)
It illustrates that many of these breaches leak far more than just "only amounts to my email address" ... "and the specific password for the compromised site" as you put it.
Remember also that for many people affected by breaches, the leaked data would lead to compromise of other unrelated sites due to re-use of credentials.