If you incinerate the trash instead of burying it, carbon does indeed get released.
If you burned enough coal/naturalgas/oil to produce the same amount of energy produced by incinerating, you would release a comparable amount of carbon.
Burying it doesn't sequester anything, if you assume it gets burnt to produce energy. If you burn it, you displace burning fossil fuels.
I wish recycling was more realistic, it frustrates me to no end that out of all those cute numbers that indicate you should feel good putting it in the recycling bin, odds are that anything you put in made of 3, 4, 5 (sort of), 6, or 7 is counterproductive. It just contaminates the good stuff.
But tangent aside, if you consider the plastics to be fuel it makes absolutely no sense to sequester them instead of burning them to displace fossil fuel use, reduce land use, and also centralize a major pollution source (plastics and such contaminating groundwater near landfills over centuries vs a centralized emissions filter).
It seems like a lot is simple once most electricity has a low marginal cost (environmentally, of course they'd usually negotiate feed-in tariffs or other guaranteed long term pricing that accounts for the capital costs of construction).
Landfill seems to be the contrarian's choice but this appears to some anti-regulation propaganda after effect.
Headlines like "Thing you do to save the planet actually hurts the planet" is like catnip for some people, and they dont ask any awkward questions about who is claiming this and why.