It's "just" carbohydrates - in theory it's no worse than burning oil or gas for heating/electricity, if you make sure everything burns at high enough temperature to burn cleanly and have filters at the exhaust to catch anything that survived the processes.

I'd say it's a positive, we use oil to produce plastics, if that oil is used to produce energy after its plastic form is no longer needed....that's a plus in my book. But maybe on the other hand it's better if it stays in the landfill instead of being burnt and releasing the bound carbon into the atmosphere.

A modern plant turns plastic into CO_2, electricity, and, often, residential heat. So, yes, that's preferable. Among the sheer ugliness and wastefulness of landfills, burning at high temperature avoids the toxic intermediates plastics give off when degrading in nature, which landfills struggle to contain.

Ash is, by definition, inert. It is the remaining mass that does not chemically react even under extreme heat. It therefore also does not interact with, for example, the human body. Plastics are all carbon/hydrogen/nitrogen/oxygen, and, to a first approximation, do not leave any ash. In reality they do, but it's extremely little and harmless.

(Physical harms can survive an incinerator, such as material giving off radiation, but those should never be in the trash)

Incinerator ash and fume often has a very high concentration of heavy metals, comparable to coal ash. Definitely not harmless.

You're correct that sufficient incineration temperatures ensure the complete destruction of organic intermediaries, such as dioxins.

I cannot put a source to it but I remeber to have heard the ash landfills (that are hermetically sealed) are designed to be resource deposites once they are full. It does not make sense to recycle the involved metals etc. while its almost empty but should be worthwile once a large deposite is established.

From a C02 perspective, if it's burned cleanly and the energy released is used to generate electricity or heat homes, it's really not much different than a natural gas plant. But I agree with your point.