So when I’m asked to obsessively clean out my aluminum recycling, I’ve always assumed that’s just a favour to their equipment. But surely the process expects FOD and messy cans.

It's staged and transported. So like the less food there is at the collection site the less stink and rodents there will be.

Additionally the health and safety of workers from direct biohazard contamination.

I've always wondered this. In my small town in The Netherlands, plastic and metal go in the same recycling sack. They specifically state that you don't need to obsessively clean the containers, but they should be "empty". I'm sure I've accidentally tossed some paper in there, but I assume that gets burned away at some point.

But how they sort it afterwards? I have no idea. Not all metal is conductive, though I have to assume they do some magnetized sorting. Plastic can probably be blown away for sorting further down the line.

Might need to explore this more in the near future!

There's a whole process. In the US, "Bulk Handling Systems" seems to be the leading company in the sorting of recyclables. There are shredders, shakers, air separators to pull out the light stuff, DC magnets for ferrous metals, AC magnets for aluminum, multispectral vision sorters for different plastics, and even AI vision guided robot pickers. Most of the sorting is done with big, simple machines. The robotics just picks out unwanted stuff missed by the earlier steps to give clean product that can be sold. That was a big insight in this business - you need some machine intelligence, but it's a small part of the overall system.

It's simpler and cheaper to machine sort the stuff at one location than have lots of little bins into which people mis-sort stuff. Most of the cost is out collecting the stuff, not sorting it, and single-stream recycling simplifies the collecting.

Look in to how a materials recovery facility works https://en.m.wikipedia.org/wiki/Materials_recovery_facility

My city has one and there are several others serving smaller areas, recycling is commingled and mixed materials are accepted.

My thought was the melting process burns most of it off and then the ash gets skimmed off the top.

not worth it to clean yourself.

Isn't most plastic we'd think of recycling (bottles, food containers, utensils, etc) thermoplastic, and able to melted and reformed like you described?