A filament extruder is essentially an injection molding extruder head without the press and mold - it's pretty advanced technology that requires integrating thermal design, mechanical components, and precise electronic monitoring and control. To get anything close to consistent output you're probably going to need a lot of special cutting and extrusion screws and probably some kind of additional pressurization system, and then the user still has to be disciplined about sorting and cleaning their plastics to get a probably mediocre output. Something like: https://www.instructables.com/Recycled-PLA-Sheets-From-3D-Pr... might be a more practical recycling paradigm for 3D printer waste.

If you heated with wood you could just burn it (and a whole lot of other things). Obviously not ideal above a certain population density...