I always drink mine but if I have to dispose of someone else's I always pour if possible and stuff with napkins if not. The bin changes nothing, gdansk. At some point it must leave the bin. Durr.
I once ran a continental breakfast at Comfort Suites and had a bag full of coffee rupture while trying to lift it into the dumpster. It didn't help that the millionaire owner's kids were visiting the USA and were hiding in the bushes throwing rocks at me. My brand new Gameboy Pocket was dripping coffee from the speaker and the buttons were sticky from then on.
I also catered fancy places with my sister in San Diego. We'd collect the cups and plates from the table early so that people would feel serviced and attended to, but it also meant much less cleanup at the end of the day and it also meant we were able to dump fluids without making a giant pitcher out of our trash bins.
When we would collect the drinks left over at the end we would go around collecting the remnants of many drinks in a few pitchers and stacking the cups. When we used disposable cups, this also reduced the number of trash bags we needed significantly (hundreds of stacked cups fit in one trash bag where hundreds of semi-full cups haphazardly thrown in bags will take several).
I think gdansk is a liar who feels less guilty about doing that to the people who have to clean it up as long as he gets everyone else to follow suit.

Not every trash can can be wheeled to the dumpster, you know. Even when you make it there, as I have demonstrated, it may not be enough.