Randomised passwords would be a nightmare in the company I work for. I imagine hundreds if not thousands of requests to Group Tech for forgotten passwords on the daily.
That said I think Lastpass are right in saying how the way of doing things now is broken.
At my workplace they block passwords using portion of name or surname in it and some other things. They should also block months being used as passwords.
The problem is unless there is some system it gets too hard to remember.
I still think the future should be the way phones are unlocking these days. Simple fingerprint reader. No password required. Perhaps a security pin that does not expire often then.