<p>Is there such thing as a 3D printer with a very large diameter nozzle, that can make low fidelity, large and fast prints? I'm picturing a soft serve ice-cream machine on a gantry, with a hopper.  You feed it shredded plastic, and it prints bricks, or boards.</p>

You can certainly get large nozzles, but the material for extrusion still needs to be consistent.  So any chunked plastic would have to be melted and that will produce an erratic flow at the extruder.
By reforming your shredded plastic into a consistent string of filament, then the printer has a steady supply of material to use.  There are already filament extruders for the small shop, but they're still expensive for the home user.  The main problems are getting consistent thickness of filament, and minimising contaminants.  Also colours tend to be lost and muddied.  These might be economical if you have a print farm and are consuming a spool a day on average.
On a large scale, there are "3d printers" that can place a special quick-drying concrete and produce small buildings as homes in a matter of days.  However they're fed a special mixture of smooth cement and accelerators to set the concrete ready for the next layer.