The problem is: There are many different kinds of plastics. All plastic can be recycled, but not all recyclers will accept every kind of plastic. They will only take plastics that are economical for them to process.
Soft plastics like plastic bags and food wraps are usually uneconomical to recycle. If they still have food scraps then they have to be washed first. This is why few recyclers will accept wraps and flimsy food containers.
The plastics have all to be separated after collection, often by hand. This takes time and is dirty work. Plastic bottle tops are made from a different plastic than the bottle, so they have to be separated. So you should always remove them before recycling.