It's amazing how many people don't understand this. I like to tell people I can give them a 100% secure firewall. Then I tell them it's called an AirGap - do you still want it? Engineers understand that everything is a tradeoff.
Everybody knows this, it's a matter of whether it's worth it or not; where you draw the line.
POF users did indeed get the convenience of a password reminder in every email. But they also got the inconvenience of having their passwords compromised, the consequences of which could both be catastrophic and go unnoticed for a long time. In summary, not a great user experience at all; thus "user experience" is a bad excuse, especially in this particular case.
Actually not. I started using 1Password and I must say it increased both, security and convenience. No temptation to reuse the same (and simple) password, easy login ("Fill and login") and password generator with which I generated absurdly complex passwords I am using now. And I don't even have to remember them!
That would be a single point of failure for your entire online life, it would seem. I've actually got no idea how one would assess where that sat on the trade-off spectrum.
What would you consider a failure? I use 1Password + Dropbox, so in effect my passwords database is backed on three computers and iPhone.
That's one additional benefit: new logins and passwords are synced.