That is one kind of categorization, but if you're wearing polyester clothing or nylon clothing, there's no recycling of that, and there's no labelling of that. If you have plastic packaging, a lot of the single-use disposable plastic packaging is not labelled.
The problem with plastics right now is that the very simple but effective approach to categorizing the seven types of plastic often fails to incorporate the issue of adulteration through chemical additives, dyes and other things that reduce the recyclability and value of that material.