There is a crisis in the household waste recycling system. China is not accepting many different kinds of waste.
Mixed paper is one. What would be the problem with burning this in power plants designed to handle it. Is it much different from wood? The same with PET bottles. PET is after all a petroleum product. I seem to remember that high temperature furnaces can burn without many emissions.
The small city I live in is going to be negotiating a new contract this next year for garbage and recycling pickup. About 2/3 of the residents get free recycling, the other 1/3 like me pay. The mayor has stated that costs for garbage pickup will be going up and free recycling will likely go away. The city is also considering stopping recycle pickup altogether and going to recycling drop off centers.
Here, the recycled mixed paper is shipped a couple miles to a paper company and turned into cardboard cereal boxes, etc. But that paper company pays less than the Chinese used to (partially offset by reduced transportation cost).
The problem is economic. There are plenty of uses for the recycled paper here – they just pay less than the Chinese did, and most recycling programs depend on the sale of the recycled output to break even.
Paper plants can use recycled mixed paper – but it’s of less quality (thus worth less) than virgin wood pulp, which is still readily & cheaply available here. Power plants could burn it (if they were designed for it (they aren’t)) but it’s less energy-dense than coal or natural gas, and produces a lot of ash.
There’s no problem in finding ways to get rid of trash. There are plenty of ways to do it, and in fact even just landfilling works just fine. When you hear about a garbage barge wandering the seas without a destination, or whatever, that’s just because of political disagreements about where to put it, not because there isn’t any place to put it.
What’s tricky is finding a way to get rid of it while also turning a profit. Ideally, you’d find someone who wants it enough that they’re willing to pay more than the cost of collecting it. For scrap metal, this is often possible. But for most other materials, it’s usually not, so you have to charge the people throwing the stuff out for the service of picking it up. Even there, you hope to at least get something for the stuff, so you can discount the pickup charge, but even that isn’t always possible.