This is especially obvious when you talk about stuff made of a lot of different materials.
Picking such things apart for different material streams is impossible to scale.
I was thinking, what if governments were mandating mandatory chemical tagging of all common materials, so you can just shred everything, and then separate materials using machines which can distinguish chemical tags.
Each manufacturer of those goods can decide how to handle their "pile", and if they design for recyclability, it's going to be easier and cheaper for them. If they can just say "combine our product with these other products made from the same material" that'll work out cheapest. If their answer is "our product contains a mix of various toxic stuff" then they're going to have to pay for some specialist to handle it... In every location this 'pile' exists in every city...
The only place this system doesn't work is for products that change state significantly during consumer use - for example a candle gets mostly burnt away, but the remaining blobs of wax are probably untracable to the original manufacturer.
There are tons of unrecyclable stuff in regular household garbage. For example, a packaging made of two incompatible in recycling methods plastics are a waste.