I could be wrong, but I'm pretty sure what makes recycling expensive is that when we don't sort or wash things, the recyclers have to do it.
Why do either of us need to do it by hand, though? Sorting metals and glass from paper and plastic shouldn't be that hard to do mechanically. They have different densities, for one thing. There has to be a way to use that. Or perhaps a machine that puts all the junk through a narrow passage that opens somewhere else whenever it detects a "clink." Then there's at least a great deal less stuff to handsort. If it works well enough without the handsorting, you could just push all the glass and metals apart with the lenz effect. That's two categories done.
Separating paper from plastic is a bit trickier if you want to actually keep using the paper, but why? Paper is easily the least necessary thing to recycle. We plant more trees to specifically to become paper than we cut down to make it. Soak all the paper and plastic garbage together. Anything that becomes a bunch of disgusting mush is paper, with mostly food waste stuck to it. Fish the plastic out of the slurry, let the evil papier mache dry, chop it up and do basically whatever you want with it, up to and including throwing it out the window. It's biodegradable. It's not good mulch, but it can be part of mulch. Or fuel. Or some kind packing or building material, if you vacuum seal it or something. I don't know. Nobody should care. It's paper.
The point is, after you do all that, you have the plastic, or at least you have stuff that is mostly the lion's share of the plastic from what you collected. And that's the problem material. It's the crap you need to do something with that is very hard to make money off of. Why are we handwashing it? Slice all the containers to bits, then boil the shit out of them. Done. Now you have a whole bunch of plastic that the Chinese can melt down and... do whatever it is they do with it.
