Disclaimer up front, I work in waste treatment (EU), and at work we separate waste for recycling, we burn waste, we compost organic waste, we operate organic digesters and we operate land fills. Also, I'm rambling in the text below.

So regarding separation of packaging waste, it's doable. Automated separating works pretty reliable, and we can get plastics like PET out of the waste at 98+% purity. Second biggest problem is stuff that doesn't belong in the stream to be separated, people throwing stuff in the wrong bins. Biggest problem however is money and the politics behind it. Since oil companies are higly subsidized, and plastic producers are closely related, so called virgin plastics are dirt cheap. They're so cheap, that plastic manufacterors are finding novel ways to use plastics every day where ther really is no need to use them. I mean stuff like cookies invidually wrapped in plastics and then packaged by 6 or 8 in tray which is wrapped in plastic. At some point all this stuff gets thrown away, and my employer comes and the plastics then need to be separated from the other waste. This costs money, and the gate fee for waste doesn't cover this, it's cheaper to burn the waste and produce energy from the generated heat. It would be even cheaper to put the waste in a landfill, but there's laws against that, today only stuff that can't be handled in any other way is allowed to go to landfills where I live.

So who pays for this? The government! In the EU countries have all kinds of environmental ruling, which are translated into laws for every country. The countries could basically rule that the producer of polluting materials have to pay for the clean up, but then you're threatening oil companies, so the lobby industry dealt with that. Same goes for plastic producers. Now all that's left is waste treatment companies and civilians. The waste treatment companies aren't in the business to lose money, so it comes to the civilians. Of course it's hard to sell to the people that they need to pay for all of this, so how do you deal with this? You start a semi-government company to handle the separation and recycling with subsidies for the companies doing it. So far so good. So where does it go down hill? Well, where everything goes wrong!

In general, the semi-government company (SGC for brevity) gets his money from the government, and pays the for profit companies to do the job. To check if requirements are met, the SGC's budget is controlled, and the allmighty god of metrics is summoned to check if everything is running ok. The metrics turn into KPI's, and KPI's will become their own goal. So the SGC now has goals it needs to reach to get funding, and it will work to meet these goals. It does so by introducing lots of different KPI's througout the waste management chain, and (for example) in the process allow the waste collector to mix in industrial waste into household plastic waste to get more volume, snce this is a metric by the government. Then the seperation plant has to put in more effort into their process generating more reject and a less pure end product, which gets harder to recycle. Meanwhile the SGC gets a lot of slack from the government for not meeting its targets.

All in all a big wall of text which seems to go nowhere. However, my opinion is, if laws would be made to reduce plastic up front and to tax companies for envornmental impact, the waste industry wouldn't need to be as convoluted as it is. It would would mean less virgin plastics produced which leads to less demand for recycling. I'd still have a job since waste will always be around, but the fossil industry and the money behind it might take a hit.

They're quite difficult to sort by type though. For the consumer and the recycling company.

You can turn PET bottles into a string and use it in your 3d printer.

Which is basically irrelevant, since you need to dope the recycled plastic with fresh plastic for most applications and no one is doing this at a meaningful scale

And even if we did scale it up, this just means the amount of plastic use will continue to increase. We'd have to find uses for the lower strength and quality plastic even

You misspelt weird.

Neoliberalism at its finest.

I ask you to consider researching the origin of recycling plastic in America (US).