Nothing wrong with IQ tests at all, in fact we perform them all the time, maybe we call them coding tests, take home projects, or whiteboard interviews from time to time, but they are still a very effective measure of ability.

Each of these has a way to eliminate people I have no reason to hire, including timid/shy people with no backbone of their own, people who are terrible at communicating, people who are clearly out of their depth even in a low stakes environment on a toy problem that doesn't even need to be fully solved.

Communicating clearly doesn't require a high IQ at all, it's a general skill. If anything, high intelligence might be a detriment since a lot of the smarter people I've known can't or refuse to communicate clearly.