Now it's all faux-compostable plastic and polystyrene for some unfathomable reason which all has to get thrown in the trash even though they have "compost bins" that I know from calling around can't even handle the "compostable" plastic provided in the cafeteria.
Probably literally millions of containers thrown in the trash over the last fifteen years because they didn't want to pay a dishwasher... just doesn't even make economic sense...
The other hack is that the cost of trash disposal is artificially depressed to reduce the incentive to dispose of refuse by illegal dumping. But this means refuse is overproduced.
Recycling is an attempt to reduce this increased volume of refuse going into landfills.
The better strategy would be to charge a fee, up front, for all goods that reflects their cost of disposal. This would be used to subsidize disposal in whatever way was most economical (recycling, landfilling, incineration). It would discourage overpackaging and encourage products that were easier to dispose of.
If the tax depended on e.g. volume of packaging vs volume of content, or weight of packaging vs weight of content, that might be a different story and more useful. But even then not all trash is done equal, a paper envelope or cardboard is way better than a plastic one, even if it's bigger/heavier.
Why is it better? Because the plastic comes from fossil fuels that cause CO2 emissions? The solution there is a CO2 tax on fossil fuels, not trying to special case the waste disposal fee.
But GP isn't entirely correct. There's less problem with stuff that can remain unchanged (you can bury it and forget it, or use it as filler for construction, etc.). The problem is stuff that decomposes into toxic compounds, poisoning the ground and risking poisoning drinking water. And the other problem is stuff that gets shredded by UV rays over time into microscopic particles that then gets eaten by small fish/animal, and ends up being present in organisms all across the food chain. The particular case of the latter is microplastics, and AFAIK we aren't yet sure if they cause any concrete problems to living things, but it's probably still better to not have them in our bodies.
...and back to those things that don't decompose at all: it's a potential problem long-term, because we're just throwing away matter exponentially fast. You can imagine life in modern capitalist countries as one fat pipeline of: Raw resources => Factory => Brief use => Landfill. And that pipeline is pushing exponentially growing amount of matter through it. And then ask yourself, how is this a sane way of living? It's a machine that quite literally turns the surface of Earth into a pile of waste.
That's exactly how it's done in multiple European countries (IIRC Netherlands was the pioneer there, but there are others) - there's a tax on packaging and in some cases disposable plastic stuff, it gets collected at the point of manufacture or first sale and is used to subsidize sorting/collecting/recycling or reprocessing or incineration, just as you propose.
Alternatively, there are schemes such as Germany where the manufacturers are responsible for ensuring that their packaging gets mostly collected and reprocessed afterwards, so instead of a tax, most manufacturers cooperate to directly fund a private program ('green dot') which organizes collection from households and recycling/reprocessing/other elimination of that packaging waste.
This year I learned with my own eyes how that fee is spent. The landfill buys a shredder ($300,000+) a conveyor ($50,000+) to stack a big pile and a wheel loader ($200,000+) to sprinkle the shreds into the incoming trash stream.
Non-productive and energy intensive green wash with the material ending up in the same place. But it is no longer "whole".
gimmeabreak
I believe one of the more effective diversions is cardboard (where recycling it at slight income is better than spending resources burying it).
Last I knew, it's many metals, some paper, and some glass that are typically net benefit to recycle (from an energy perspective.) Plastics tend to be a lot tougher because of the energy requirements (transporting, cleaning, etc.)