I used to work designing landfills and they're not a bad choice. Right now many landfills in the us are the worlds largest bags. They definitely are now better engineered so that toxic substances have less chance of leaching into the ground.

They roll out large sheets of plastic and weld them together. Some states (NY) require dual liners (bags in a bag) and piping to collect the liquid that comes out at the bottom "(leachate). When they put the plastic top on holes are made to allow waste gas to escape. Landfills tend to be dry and nothing rots in them.

I think they work well, but its better to reduce the waste going into them. I'm assuming many places in the world aren't handling the trash like this leading to issues with groundwater contamination and other problems.