On the other hand, in Japan there are extremely few places with public trash cans. Those few that exist are typically associated with vending machines for beverages.
IIRC they removed them after a terrorist attack in the 90s.
I'd assume that these days the lack of desire is mostly a matter of funding. Possibly also something about reducing the number of crows/rats digging through trash.
Japan also has a rather strict trash sorting system, and not having public trash cans might serve as a forcing function to sort things properly (since if you get it wrong things will be attributed to you). Similarly it's possible that under some circumstances, under-serviced public trash cans could end up increasing the amount of litter on streets: people may be more likely to stuff things into an overflowing trash can (or dump stuff next to it) rather than carrying it with them.
It was a good time for Japan, but unfortunately there was a horrible side effect.
No one could get a hold of the cans, to empty them.
Soon trash overflowed the cans, just as you said! Admitting defeat, the cans were eventually blown to pieces. This explains why Japan has trash on the streets, and why Japan had overflowing trash cans.
But this is all fixed now. As you know, Japan has no litter, and no one would ever stoop so low as to liter on purpose.
As for trash cans, many train stations I use have bins located near the entry/exit gate where you can put it in the correct slot (burnable, plastic, bottle, etc).