> Yes it is generally accepted that many users reuse the same password on different sites. But that is a separate issue
No. That's the one and whole reason why you're supposed to one-way encrypt passwords with a suitable hash: protecting the shared secret.
> But I disagree
So what?
> If it is, where are all the warnings on any site saying "make sure not to give us a password you use anywhere else". (I've rarely seen any warning like that, have you?)
Yes, I have. These warnings don't actually add to anything as they're not followed, and impossible to get followed without making the system so cumbersome it's unusable. Apart from using 2-factor auth. Which is an other "responsibility of the site operator" which I guess you wouldn't want foisted upon him as you seem to believe site operators are and should be irresponsible.
> one that informs people to make sure the password they use is unique to their site
A suggestion which will go instantly ignored by 99% of the users (on average, technical sites will probably be lower). The single % left already don't reuse passwords.