Obviously there's no 100% secure approach, but at least this makes me sleep better knowing that if LastPass were comprimized, my stored gmail, bank, paypal, work, etc. passwords wouldn't work.
I think the biggest security failure is session cookies that expire too quickly or too eagerly. Having people need to enter their password so often is more dangerous than keeping them logged in (from the same IP) for a longer period of time.
If my bank would keep me authorized for basic access (review transactions, pay bills, transfer money between own accounts) without logging in each time, but required a password to add a payee or make changes to the account, I’d keep the password in a journal in a safe.
I'm not saying it's the wrong way to go but if electronic password managers "never made sense" then I feel like you don't have the entire picture.