I have 524 passwords in my vault. That's a list large enough to require a big sheet of paper that's very inconvenient to carry around. I'm also changing passwords often enough such that keeping track of which password I changed on what machine in order to just carry deltas with me and updating my hand-written lists manually is way too inconvenient.

Syncing password managers solve all these issues and, if they do encryption right, there is nothing that could possibly happen even if they are hacked and an attacker gains access to my encrypted data.

The doing it right part is why I was asking my questions with regards to PBKDF2.