No. The problem is way more foundational than that.
You can't test for intelligence because you don't know what intelligence is. That which you are testing for becomes normative for intelligence. This is called Goodhart's law.
This is the pitfall of all positive definitions. If you are going to define positive traits for intelligence (what intelligence is), you also have to define negative traits too (what intelligence isn't).
It is precisely because you can't define what intelligence is, is why you keep falling into circular reasoning. Nobody can define what anything is - that is why all language is circular.