Do they sequester the massive amounts of CO2 that trash burning generates? If not, sinking that carbon into the ground may be a better idea. Or not: landfills produce methane and other natural gases which are more potent than carbon dioxide if they're not captured and reused. Has anyone done the math?
Most of a typical waste stream consists of current/recent biomass -- a surprising amount by both volume and weight is paper and paper products.
Plastics and such do represent fossilized carbon (usually) but are a smaller percentage overall.
So the net carbon impact is much lower than burning fossil fuels. And yes, the methane reduction helps, though methane does have a pretty short (about a decade) residency in the atmosphere as I understand.