There isn’t one main reason why our fair city has so few places to dump your trash – rather, it’s a culmination of factors. Our stringent recycling system (combustibles, non-combustibles, cans, PET bottles, plastics...) means that we wouldn’t just need a bin here or there; we would need bins for all different types of waste, and pray that people actually use them properly. Moreover, the different types of waste are collected on different days of the week depending on where you live, plus the waste classification system itself may differ ward to ward. Who knew waste disposal could be so complex.
Other than that, as in other big cities, a number of bins in public places were removed after the 1995 sarin attack on the Tokyo Metro to lessen their possible use in terrorist attacks. So for now, do as Tokyoites do and just carry your rubbish with you until you can dispose of it properly at home. Whatever you do, don’t drop it on the floor – Tokyoites are proud of the city’s litter-free streets.
If you really, really can't wait to get rid of your trash, try a convenience store, but don't go too crazy. Most stores will have a sign asking you to refrain from dumping your home waste. So to make their life easier, keep it to a minimum, and of course, sort it properly for some extra good tourist points.