If you say "Republicans don't just hate illegal immigrants" it's pretty isomorphic to "All Republicans don't just hate illegal immigrants". Maybe that's English 102.
No, "Teachers use chalk daily" is nowhere near true. It would've been mostly true 30 years ago, before whiteboards, and now it's definitely not the case. The hair you're splitting only works when the approximation that omits the "all" is close to 100%.