I think this is the most important reason for IQ tests to exist:

I've underestimated people who were bright enough but didn't present as intellectual

This is what many people do, all the time. (Even to themselves.) In extreme case, a school suspects that one of their students is mentally retarded and sends them to a psychologist... and the psychologist finds out that actually the child has a very high IQ. But there are also people with high IQ who use their social skills to hide this part of their personality and become invisible in the crowd; probably because the alternative is being alone. What a waste of brainpower!

Without the IQ tests, most people would judge intelligence by similarity with Hollywood stereotypes. They certaintly wouldn't stop trying to divide people to smarter and dumber. There just wouldn't be any other scale to prove them wrong.