Ordinary physical recycling of plastics (melt them down) runs into problems because plastics get mixed and mixed with contaminants and because the molecular chains get damaged and break down over time.

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.

3) use the best-effort stream of materials to manufacture bulk materials where a small quantity of chemicals that refuse to bond to each other doesn't compromise the product.

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.