If they do it via "pyrolyse" (burning plastic without oxygen) there is this Quantafuel [1] doing this in "large scale".
There are two approaches to chemical recycling.
One of them is to reverse the polymerization process and produce the monomer. This can be purified and used to make virgin quality plastic.
The other one is like what you describe and produces outputs similar to a petrochemical factory that can be used to make all sorts of things.
Both of the above processes are still terribly expensive and environmentally dirty but they are the subject of very active research and they might get practical someday.
Those plastic park benches and decking material products are using a lot of plastic to overcome statistics. But the perverse incentive is that a product that uses a lot of your material per consumer looks much better on paper than it is in real life. Instead of twenty shirts or fifty detergent bottles we made one bench, that goes to the landfill when it's done because it's not cradle-to-cradle.
The salts and acids are a problem that prevents commercial use, because it turns out corrosion, heat, and pressure are the 'pick two' of ceramic materials. Last I read someone was trying to work around this problem by building a heat and pressure optimized vessel and coating it with a corrosion (and?) resistant glazing. I imagine getting the thermal expansion for the two materials to be identical is a right difficult problem.