In my city (a suburb of LA), the trash contractor says they don’t have separate bins because they “separate recycling at the facility”. What a joke! As if they’ve got someone going through your trash like a raccoon, picking out the bottles.
I get that the plastics industry has an interest in making recycling appear seamless and efficient, but what a crock.
You can buy hardware which does a lot of the sorting†, and you can pay minimum wage for people to pick harder-to-identify elements out of what's left. There really are plenty of sites doing that.
† The very easiest is steel which you just sort with magnets, but aluminium is more valuable and it's not that hard for machines to sort it, paper/ board can often be machine sorted too.
There's definitely sorting going on (including hardware, such as magnet, utilizing gravity/shaking, chemical) but still plastic often ends up in landfill because it's not profitable. Even China who used to do "hire minimum wage workers" to do recycling but at global scale ended it because all the adverse health/environmental effect making it worse than not profitable [1]
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.
I get that the plastics industry has an interest in making recycling appear seamless and efficient, but what a crock.