Well, not quite wherever they stood, there was a dump, but yes, it was not until the 1880s that people in the US began to even consider solid waste something that required state/government action to organize and resolve in major industrial cities in the east, primarily motivated over concerns of public health from various epidemics. Those were new ideas in major cities, much less the frontier west. New York City was the first American city with a public waste disposal service (there had been private services that wealthy neighborhoods hired), and that wasn't until 1895. It's hard to imagine how *awful* 19th century American cities would have smelled pre-mechanization/cars, as horses and the various animals brought in for slaughter simply excreted waste wherever they stood; tins for canned goods and any other manner of material waste was often simply tossed wherever they would be out of the way (or more accurately, out of the way of whoever discarded it); animals that died were sometimes just left to rot in the street or be scavenged by stray dogs - there's a famous picture of a dead horse in a NYC street near children playing (admittedly that photo dates to 1905 but it was quite normal before instituting public waste disposal). Here's an article interviewing Robin Nagle, an anthropologist with NYU, about her book, "Picking Up", about the effort to build a public waste management process in New York. The amount of trash NYC produced was prodigious - here's an article from the New York Times in 1886 detailing how Rikers Island was expanded/built from landfill by depositing all the 'ash' (street waste) that private cleaning entities collected in the city.

I can't find a source for it online, but I recall reading in a book on the American frontier that travelers could gauge the age and stability of a frontier boom town from the size of the tin can dump - bigger dumps meant the town was either longer standing or whatever was driving the boom was big, because new towns didn't have the farms to support all the people and so they relied on importing canned food. A tangent, but an interesting bit of scholarship about the history and industrialization of canning, starting from 1810 which I'd hoped had more resources on disposal (but which sadly doesn't go into it from what I read).