First you'd have to demonstrate that intelligence is multi-dimensional, at which point you'd still fail since you can represent any point in any number of dimensions by single numbers. Hilbert curves are a trivial mapping. The entire field of manifold embedding exists as a counterpoint to your claim.
And, as others point out, it's also possible that one or a few values capture increasingly larger and larger amounts of the entire effect.
Claiming high dimensional items aren't describable with a single number is simply mathematically wrong.
If you have two scales and used them to weight the difference in mass of two objects, and one says there is a difference and the other doesn’t, you cannot just conclude that there must not be any difference. Obviously one scale is wrong. So in this case we have to ask which scale is wrong, the collective results of hundreds of well documented scientifically conducted studies or your “gut feeling”.
I had classmates who were quite smart in interpersonal communication, but really struggled with abstract tasks in mathematics or physics. One of them is a fairly successful businessman now, but still shudders when someone says "Pythagorean theorem" aloud.
Given how heavily do IQ tests lean on geometry and abstract pattern matching, he might score rather low.
Secondly I'd recommend making an effort to travel to these "low IQ countries". I can assure you the average person is not much dumber than the average American.