Taiwan's policy, related to trash, is that you are expected to take your trash home and dispose of it properly, that is, using the correct bin for separate collection of different types of trash.
This is part of a rather comprehensive policy on how to process trash, after, years ago, Taipei's streets were lined with trash and very stinky.
A podcast called "...
Have a look at Star singers and Chalking the door (both Wikipedia):
Chalking the door is a Christian Epiphanytide tradition used in order to bless one's home, as well as a Scottish custom of landlord and tenant law.
Either on Twelfth Night (January 5), the twelfth day of Christmastide and eve of the feast of the Epiphany, or on Epiphany ...
In Japan it is a standard greeting, for example when you meet someone in the evening and have a drink, when you finished work for the day, when congratulating someone for having finished some project:
お疲れ様です otsukaresama desu
which means something like "you are tired", but is better translated to something like "Good work!"/"You're working hard!"
Taiwan has more expensive official trash bags which are needed to throw out non-separated trash. Separated waste can be put in any cheap bag. If people would have free public trashcans, this won't help encourage recycling.
Another reason is that the trashcans will attract insects and rats.
I guess you can speculate, and a Japanese person will probably come up with a justification.
But the most likely explanation is: It's is considered bad manners for no particular reason.
If a Japanese person asks you why Westerners consider it rude to slurp soup - which Japanese people regularly do - there wouldn't be a reason to that either. Or rather, ...