I don't mean IQ as a number, I mean the underlying g.
And people who graduate college and start working neither do, nor are expected to "solve novel technical problems". The closest to that are programmers who do have to solve problems daily, but for them courses in e.g. data structures or just experience with radically different languages will develop much more useful intuitions than "mathematical sophistication".
If you are going to become a mathematician or a logician, by all means go study proofs. Otherwise I don't think they justify the opportunity costs.
When Heinlein said "specialization is for insects" I think he was making a similar point about metaskills.
Aren't you suggesting specializing in a particular metaskill?
I think g is sort of a mathematical artifact, not a real thing (but don't really feel like getting into a big thing about this). Factor analysis doesn't tell people what they think it does.