Maybe it takes more energy because of the diversity of materials? If we used an order of magnitude less types of plastic than we currently do, it might become more economical because it wouldnt require as much mechanical labor to sort and process. Removing shipping from the equation seems like the removal of quite a bit of carbon.
When you melt plastic down, you get lower quality material than what you fed in. It's not a closed loop. Plus, the wide variety of available properties are what makes plastic so useful in the first place.
Asian companies undercut all the domestic recyclers, putting them out of business. This is why you might not want to trust say Chinese companies with prices that are too good to be true (because they are probably cutting huge corners somewhere). The same thing happened with rare earths (very dirty to refine, but China didn’t really care about their environment giving them a huge price advantage that shut everyone in the developed world down).
Plastic and Glass recycling can be borderline and it depends on the specific local implementation. Either way, the savings are never going to be massive and it is an open question if it is worth the effort. (Glass re-use is different)
Aluminum is completely different. Prices for aluminum recycling per ton is an order of magnitude higher than other recyclables.
What's even better than putting your plastic bottle in recycle is not using plastic bottle at all. Is there any use case where plastic bottle is better or required?
Apparently manufacturing glass uses way more resources/energy and has a much bigger carbon footprint. (No source at hand, sorry.) It also weighs more so is more expensive to transport. Plastic is good for some things, no doubt about that.
