Do people actually use hard mode? Seems like its only "harder" in the sense that it forces you to play less intelligently.

This is why I turned it off. It is "hard mode" in the same way that driving a screw with a hammer is "hard mode."

I find it fun because it prompts me to find the optimal guess (given hard mode). Playing easy mode I'm much more happy to do the first word that comes to mind and sort of fits.

Hard mode emphasizes vocabulary over math.