They aren't being used wrong. It's just that no one will say it's OK to use them that way for liability purposes for when someone inevitably screws it up or already has too much wax. It also depends on what type of wax your ears make (people have different kinds. Wet, dry, or somewhere in between)

I've used them for decades "the wrong way" and checked my ear canal with a little bluetooth camera thing made for ears. My canal and eardrums are immaculate, so it happens to work great for me.

Cotton swabs were invented in the 1920s for the purpose of ear cleaning. They were marketed as such until around 1980 when the market became worried about lawsuits from people stabbing their ear drums or people with lots of wet wax built up already in their ears compacting it towards the ear drum instead of it getting cleaned out.