This is a very controversial question. Any answer that we can give will be disputed by some people.
First of all, the term “academic capability” is itself a difficult one to define. It is very hard to know exactly what shows that a student has academic capability. For example, if a student is very smart but does poorly because they do not care very much, do they have “academic capability?” Therefore, it is going to be hard to answer this question because there is no single thing that can really be identified as “academic capability.”
So what does the SAT measure? It is not meant to be a measure of intelligence or IQ. It does not claim to measure innate intelligence. What it claims to measure is how good a student’s grades will be in their freshman year at college. Even there, the SAT is not a complete measure. Studies have shown that SAT scores seem to predict about 18% of the variation in students’ grades in their freshman year of college. That means that about 5/6 of the variation in students’ grades is not captured by SAT scores. SATs, then, do measure how well a student will do in college to some degree, but it is a very small degree.
The SATs (and ACTs), then, are not a really great measure of anything. They tend to continue to be used because it is much easier to look at these scores than to try to look at a student’s entire record and try to predict how well they will do in college.