I googled global waste per year. Looks like it's on the order of 2 billion tons per year. Leaving room for 100% growth, and assuming a density of 1 (less dense = more space required = worse), we'll need 4 billion cubic meters of landfill per year. That's a cubic mile of garbage! But that doesn't seem all that catastrophic either - if you spread it out to a hole 1m deep, it'll be 63 km on a side. 5m deep = 28km on a s…
Plastics and other carbon containing substances buried underground sounds terrible at face value but the thing that should really make you worry is the amount of carbon released into the atmosphere. Atmospheric pollution can often coincide with the amount of trash you create but in general if your focus is on landfill rather than atmosphere you’re focusing on something that doesn’t have a scratch in levels of importance.
In fact if we can find a way to landfill co2 rapidly in a net co2 negative way that may be our best hope right now (repeatedly growing and burying large amounts of biomass for example).