the ability to acquire skills is what IQ tests do though the use of Logic puzzles that anyone can do, that require no training.

if you can train and improve on them then they do aggregate training. I.Q tests are based on the western model of understanding the world. This is why most African countries have very low marks. This is why most indigenous people don't do good on them. Take any high I.Q person in such a country and they will starve to death because the environment requires different kind of intelligence.

and if people can do better on the tests with training then they can train themselves to be more intelligent

actually not. if they stop training the I.Q falls back. in other words, intelligence is nothing but gaining expertise on a specific way of thinking.