The way human IQ testing developed is that researchers noticed people who excel in one cognitive task tend to do well in others - the “positive manifold.” They then hypothesized a general factor, “g,” to explain this pattern. Early tests (e.g., Binet–Simon; later Stanford–Binet and Wechsler) sampled a wide range of tasks, and researchers used correlations and factor analysis to extract the common component, then norm…
Another component of this theory concerning g is that it's largely genetic, and immune to "intervention" AKA stability as you mentioned. See the classic "The Bell Curve" for a full exposition. Which makes me wonder what's the point of all the intervention in the form of teaching/parenting styles and whatnot, if g factor is nature and immutable by large? What's the logic of the educators here?
Many/most people (esp. young people) are not pushed to the limits of their capacity to learn.
Quality interventions guide people closer to these limits.