The ugly truth is that most plastics aren't really recyclable, especially not in the form of "big glob of mixed mystery-polymers with a dash of food residue and

The ugly truth is that most plastics aren't really recyclable, especially not in the form of "big glob of mixed mystery-polymers with a dash of food residue and other organics". What usually happens is it's either downcycled into a significantly lower-grade material, or depolymerized and turned into fuel. PET recycling is the one exception, where you can relatively reliably get reasonable (but lower) quality plastics back out of the process.