The hypothetical g which IQ tests are trying to find is the extent to which every test of mental abilities that anyone has ever devised plus some things like re

The hypothetical g which IQ tests are trying to find is the extent to which every test of mental abilities that anyone has ever devised plus some things like reflex speed all seem to be fairly strongly correlated with each other and all seem to be correlated via a common factor. You can certainly be more skilled at one test than another. These tests are also fairly noisy when applied to individuals. For individuals the results of IQ tests probably are oversold as you say given their noisiness. But for public health problems like air pollution where the results are averaged over populations they're probably undervalued if anything.