In my admittedly anecdotal experience, the rate of full grown adults who casually ignore the sinks after finishing up their business and leaving a stall seems to be disturbingly high. It just kinda gets my ick-factor going. Granted, I'm something of a germaphobe (I wash my hands many times/day) so I might just be more inclined to notice those who don't vs those who do--- regardless, I'll almost always save a paper towel or something to turn the door handle when possible.
Anyway, I don't think the lack of a trash can nearby excuses those who would dispose of it on the floor though. I just hold onto it until I find the next closest trash can outside the bathroom. That usually takes less than a minute, depending on where I am.