There is some evidence that bodily-kinesthetic and musical ability does not correlate that well will g as other things, but they're still very correlated.

See for instance:

Castejon, J. L., Perez, A. M., & Gilar, R. (2010). Confirmatory factor analysis of Project Spectrum activities. A second-order g factor or multiple intelligences?. Intelligence, 38(5), 481-496.

Visser, B. A., Ashton, M. C., & Vernon, P. A. (2006). Beyond g: Putting multiple intelligences theory to the test. Intelligence, 34(5), 487-502.

Thank you for this! Very interesting.

You're making the same mistake of conflating 'good' with 'scores high on a measure'.

What is something that you can be demonstrably good at, that is immeasurable?

Virtually everything even slightly abstracted from directly quantifiable tasks: sporting skill, driving skill, intelligence, etc. None of those are measurable without significant confounding or a 'dumbing down' to some adjacent task (that still probably suffers from some degree of confounding via 'teaching to the test'). Sport performance depends on your cohort, driving accident rates depend on your environment, intelligence tests have a learned component, etc. Trying to develop a system that allows rank-ordering of ability along an axis that isn't subject to influence from an irrelevant external factor is impossible.

It kinda sounds like you're using "abstracted" to mean "poorly defined".