Yup, this is a service that already exists in very informal ways. Check craigslist for "trash and junk removal".
Having had a garage I recently organized and about a pickup load full of trash/recyclables I would have absolutely loved such a service vs. trying to find someone non-flaky on CL to actually show up when they said they would.
That's what I did when I moved back from SF => NYC. But it occupied a few hours of my time to send emails, wait for responses, try to negotiate time / price. Time I did not have. If I could open a spend 10 minutes, it would be worthwhile in some situations.
Having had a garage I recently organized and about a pickup load full of trash/recyclables I would have absolutely loved such a service vs. trying to find someone non-flaky on CL to actually show up when they said they would.