Measuring wealth is an excellent example. GDP might correlated with other measures of wealth, but it hardly explains the whole story. It can be useful in models but you can’t summarize nation’s wealth by only looking at GDP. Similarly IQ can be a useful tool. IQ tests can be used to find people with mental disabilities so that appropriate accommodations can be provided (although most of the time, there are easier, cheaper and better tools to diagnose mental disabilities). However by looking at the IQ alone (especially around and above the mean) you really can’t say much about about the mental capabilities of a person, only correlations of varying usefulness..
There is an important distinction though. I would argue that GDP (arguably) proves it’s usefulness in different economic models. However the same cannot be extended to IQs. I don’t know of many psychological models which use IQ (or any notion of general intelligence for that matter) to explain behavior (other then a hacks trying to prove the superiority of the white race, but let’s ignore those, what they are doing, it is not science).