Moving on doesn't increase or decrease the need to know what your iterations were.
Moving on is probably a good call but it has some things in common with staying with LP:
An example of something that is different for people who are staying:
*It can matter if someone got in with the password and then you changed it. There are a ton of reasons, but some of them include changes to security questions, changes/ additions to recovery email, transactions made, and phishing traps armed and/ or set.