Get everyone to dump their crap into one pile and actually invest in industrial processes to sort the crap out.
Huge con: this is a complex problem with possibly poisonous/explosive ramifications if it goes wrong.
Huge Pro: If we can solve this issue, that is a society changing capability, forevermore.
Or until armageddon/robot overlords/singularity/zombie plague at least.
We are asked to do hundreds of little things that mildly inconvenience us in order to maintain some social contract. Sure they could be made easier/nonexistent with better technology, but I:
1) don't see why asking people to do their part is silly
2) don't see why this particular problem would be more frustrating than e.g. the others I've mentioned. I feel like they are all similar on the "effort" scale.
Although I guess I'd admit that asking people to sort recycling properly is very different than relying on them to.
But I don't think this is a good system of caring for our environment. If we cared properly, rather than half-arsing it we'd have a proper industrial system with known outputs that we could improve upon. Instead we seem to have a "feel good you did your part, now forget about it" process. I guess it is shambling it's way to something more but it doesn't seem like it's in a rush - kinda the same way the world agrees on acting on climate change but no one is in a rush.
If 10% of people don't put their cart away, then 90% of carts still get put away. If 10% put things into the recycling bin that shouldn't go there, then 100% of that batch of material becomes unsuitable for recycling process unless expensive remediation is done first.