Most of Tokyo (and Japan) doesn't have an excessive amount of pedestrians' litter. Public garbage cans are rare, though many convenience stores and some train stations have them.
Is there litter? Yes. Is there much less than, say, Vancouver, Bangkok or London? Absolutely.
It's due to a couple things that tourists may not be used to:
-Be prepared to bring your garbage with you until you are home.
-Garbage is sorted differently in each municipality in Japan, and often the garbage bags cost money. Who is going to buy those bags and sort someone else's garbage?
-It's changing, but walking around consuming snacks, food, drinks in Japan is not that common. People do that at specific locations, thus they don't find themselves with empty food wrappers and drink cups while walking around. Thus, they don't see a need for public garbage cans.
-Crows make a quick mess of garbage here. Observing the above points means that (most) of Japan doesn't need stinky, sticky, flies-and-wasps-buzzing-around, crow-magnet garbage cans, which look almost as bad as litter everywhere.
Have you seen the litter that piles up late at night in many Japanese cities? People simply leave their trash everywhere but the city cleans it up by morning. Tokyo is one of the most littered cities I've seen at midnight compared to any western city.
Rat populations mostly aren't sustained by the sorts of trash cans that passersby toss garbage into (or fail to). They're sustained by containers carrying large amounts of residential refuse. (Consider the proportion of garbage you, personally, throw into a public trash can compared to your own trash can, especially food waste.) And I'm not well-versed on the specifics of Japanese waste processing, but I'm fairly confident they have something analogous to dumpsters and residential trash collection, even if they don't have public bins.
I don't know, there's a decent amount of rats where I live, but no outdoor dumpsters and very few public trashcans. Trash is kept indoors and brought out at the daily collection time.
I always assumed sewer access and the occasional rat-stronghold in poorly maintaned buildings was the issue.