Yes, burying plastic is one way to sequester carbon. But it will be there for thousands of years. Lets hope we have lots of space.
Burning it to recover energy emits carbon dioxide but plants can capture and convert it to carbohydrates. In the long run that might be better.
Space isn’t a problem in the US, for the most part, but expense is an issue, as modern lined landfills don’t come cheap.
Burning it to recover energy while also capturing the CO2 at the smokestack for use in industrial processes or to sequester is another route, though also expensive.