I think it's misleading to try and compress human mental abilities into a single number. There's verbal intelligence, mathematical intelligence, organizational intelligence, interpersonal intelligence, emotional intelligence, and musical intelligence to name a few. Yes, they correlate to some extent, but compressing it all to a single number leaves out too much of the variation.
Most written tests can only look at the first two. However organizational and interpersonal intelligence, much harder to test for, are very important for success in the modern world.