I use LastPass, and all of my passwords are generated by it, so I won't see any effect. Ultimately, I think adding a password generator to core is a step in the right direction. The strength meter helps to make people aware of the issue of password security, so it is only natural that we should provide a generator to help them confront the issue.

I'd really like to see WordPress force all users to have strong passwords by default (with the ability to disable), or at least all administrators.