[ESRogs]

You're right that it doesn't tell the whole story, but one of the major findings in the last century of psychology is that the one-number summary actually contains a surprising amount of information.

"Mental tests may be designed to measure different aspects of cognition. Specific domains assessed by tests include mathematical skill, verbal fluency, spatial visualization, and memory, among others. However, individuals who excel at one type of test tend to excel at other kinds of tests, too, while those who do poorly on one test tend to do so on all tests, regardless of the tests' contents."

"[G factor] is a variable that summarizes positive correlations among different cognitive tasks, reflecting the fact that an individual's performance at one type of cognitive task tends to be comparable to his or her performance at other kinds of cognitive tasks."

https://en.wikipedia.org/wiki/G_factor_(psychometrics).