Okay. So they do this in Japan. The plastic used in the wrapper is different than the plastic in the bottle. They require different processes to recycle. It’s also far more efficient for regular people to just rip it off and throw one in one bin and the other in another bin in their own homes than it is for a sorting facility to go through mountains of this stuff trying to get it right every single time. Frankly I wish more places did it this way.
I hope this explanation will make things even less infuriating.
Most European countries I've visited have at least 3 bins/bags : paper, plastic, everything else. Most cities also separate glass and aluminium. Some townhalls offer bags/containers for bio trash, that's turned into compost.
Where I live (EU) most single family homes have two bins, one for burnable normal trash and one for food and biological waste.
Recycling especially cardboard and paper, but also plastics is very common but those will have to be brought to either a very local drop off point or a local recycling/waste disposal site.
The drop off points usually have small containers for paper, plastics, metal, glass and small boxes for non rechargable batteries.
The recycling facility accepted pretty much everything that one could ever want to throw away.
Many cities just burn a lot of it. Technically “recycled” according to the definition and generates some energy, but plastic is just not great no matter how you look at it.
I don't have different plastic recycling bins, but only one.
Where in Europe do you have different ones?
Never have encountered those, at least I didn't realize it (in Spain, Portugal, Netherlands, Germany, Austria, Italy, Switzerland - although with some countries I'm maybe not completely up to date)
Edit: I was replaying to the wrong message, clicking is hard.
Sorting is way easier if you have to just pick stuff (semi automatically) from a conveyor belt vs having to pick individual object and separate the plastics (first figuring it how to do that, and also objects are all damaged).
Like plastic bottles and plastic bottles caps - it would be (or it partially is) immensely costlier to separate them by employees at the sorting site vs each of us taking the the ... or not taking the time end effort to screw the cap back on.
But to you point, in the last decade+ I only encountered non-sorted trash collection in like coastal/smol island communities (that are still developing & slowly getting recycling services).
Truth is, it doesn't matter anyway, because over 90% of plastic isn't being recycled.
This whole thing (the removable label to supposedly make the bottle more recyclable) is an exercise in futility and virtue signalling to the "green" demographic for profit, aka greenwashing.
Edit to be clear: the answer is to abolish capitalism, which is why all of this is happening in the first place.