If people have trouble contacting a business by email, they don't try to use email to fix the problem.
They very sensibly go to the web site and try by phone or Twitter or some other medium that isn't the one that isn't working.
Unfortunately, I'd guess that ~75% of the domains I try to contact about that don't have it. (And only slightly better with abuse@, for that matter.)
And then there are the shops who seem to believe that sending mail from bad addresses and publishing no public email addresses for anything is cool. I'm not fond of this solution, but have started considering them spammers and blocking them entirely. (I don't particularly care about them - if they want to send email to my systems they can put their big-pants on and join the rest of the responsible operators; I just don't like seeing services balkanizing like this.)
If you operate SMTP and I can't get through to you on postmaster@ ("yo, back off your retries," for example), I'm probably going to blacklist you. I'm not unique in the slightest. The decentralized nature of SMTP demands that I have a hotline to you, the MX operator, without having to navigate a Web site to maybe find you.
So I see no justification there for paying staff to manually filter postmaster@ spam.