Should IQ tests involve using advanced AI to help you write them?

This question misconstrues the purpose of an IQ test. IQ doesn't exist to provide a canonical ranking of humans (and LLMs) according to intelligence. They're a diagnostic measure, intended to identify people who require supports. In that individual capacity, they actually have some value. Giving people the ability to "boost" their score makes about as much sense as giving someone beta blockers before taking their blood pressure.

Meanwhile, the "Mensa"-type fixation on the upper range of the IQ scale is a cringe affectation.

I don't know why you would want to let someone use an AI when taking an IQ test. There's already debate about how useful IQ tests are for measuring intelligence. Letting someone use an AI during the test would just further muddy the waters: are you accurately testing the person's cognitive ability or their ability to feed questions into an LLM?

Do you mean to take IQ tests, or to create IQ tests?

Either way, the answer is no.

No.

There is no LLM that's as smart as a house cat so no.