A life cycle analysis might hypothetically conclude that landfills are a perfectly sustainable solution to plastic. Unfortunately a lot of this stuff makes it into the ocean instead where it will not biodegrade and will interfere with fisheries and ecosystems. Properly structured economic incentives and laws could solve this problem, as they have solved many problems in the past.
In my town, it'd be cheaper/better for the environment to landfill all the waste instead of sending it overseas to be "recycled." Our city recently prohibited placing cardboard in the trash. Something I would have thought is easily broken down...
Additionally, landfills are expensive to build and run so some municipalities are pushing recycling, composting, etc as a cost saving measure. Less trash into landfill, the longer until we have to build a new one.
Long story short, a landfill is not the same as a compost heap. Compost heaps are routinely turned over and disturbed to ensure that oxygen permeates through to the core of the heap. A landfill, on the other hand, is explicitly designed not to do that, in order to contain potentially hazardous materials that may leach out of the waste contained therein.