The cost of sorting has to then be factored in (because plastics are often not perfect hydrocarbons, they contain a variety of elements depending on bulk composition and additives). And, even perfectly sorted plastics will not burn as cleanly as freshly refined hydrocarbons, so you need to factor that cost in as well.

And for what benefit? Plastics in a land fill are a form of carbon sequestration if the alternative is burning them or fresh hydrocarbons.

IMO the value in replacing plastic use has very little to do with energy/CO2. It's more related to other health/environmental effects (microplastics, etc).