Swiss trash bag fees pay for garbage collection and improvements to the recycling infrastructure. They aren't meant to offset the damage to the Earth or some abstract puffery like that.
Paying by the bag is good. In the USA, if you live in a detached house there's normally a fixed price to get a large barrel collected weekly. The barrel is large enough to hold a week's trash from a family of four who puts no effort into reducing trash output. If you live alone and are conscious about generating trash, you get ripped off.
Hold up.. This not only varies by state, but by county and city. Some places have this built in to special assessments on property taxes, some contract with a trash company that collects fees directly, and some are a bit of a free for all with multiple trash companies providing pickup and or/dumpster service (this is more common in rural areas).
I had a place up in the mountains where we had to buy special $6 trash bags and haul it to a central dumpster ourselves, and there are those in large cities who have to deal with mob-run collection companies who bribe local politicians for monopoly rights.
TLDR; To generalize "In the USA" for something like this is impossible.