The problem with landfills is widespread, not just in USA. And the solution is simple in theory, hard in practice: we shouldn't be using landfills at all. It's hard in practice because it means:

Reducing the average amount of waste per individual. Yeah. In an economic system that encourages mindless waste.
Sorting the waste so it can be processed (recycled, composted, etc.). Waste is messy, so you need to rely on human labour (that's expensive). And people throw dangerous junk away, things the workers won't know how to deal with, things that are so oddly specific you won't be able to pile a large enough amount of it to process it further (and yet since there are multiple types, they're together a big problem). Ah, if you're composting it, give up using the compost to fertilise food crops - odds are it'll be contaminated as fuck.
Creating and maintaining facilities that process that waste. Except people nowadays really, really, really love plastic; and plastic is not just "it's plastic lol process it together", each type must be processed separately (this compounds with #2).
Deciding the less shitty way to handle what you won't process. Burning is often a solution, and often a problem on itself; let's not forget that decomposition is never complete unless you reach high temperatures (here's some additional cost!), and if it's incomplete you're releasing harmful substances in the atmosphere.

So... yeah, we got a bunch of ticking bombs, all around the world. Yay, capitalism. /s