I actually don't know of any studies of the nature I suggested. Note such a study would be fairly expensive as the cost of standardized high-quality one-on-one tutoring (with both mental and physical coaches) over a period of one year for the study cohort would be rather high, so such studies may simply not exist.

It's not soapboxing; in particular it would be interesting to see if the 'ability to learn and improve' changed with age. It's commonly assumed that it's harder to learn new things as we age, but I've never seen that data quantified personally... Hopefully it's less true than we imagine it to be.

There’s nothing “all-inclusive” - but we have really robust research for each piece of this in a vacuum, because frankly it would be incredibly difficult to test the generalizability of any single tutoring methodology when applied long-term.

This is the seminal paper on one-on-one academic tutoring from 1984 that’s spawned hundreds of follow-up papers: http://web.mit.edu/5.95/readings/bloom-two-sigma.pdf.

The biggest corpus of raw stats on age-related learning AND the generalizability of that knowledge come from the fad of brain-training games from the 2000s (e.g. https://scholar.google.com/scholar?hl=en&as_sdt=0%2C44&q=bra...).

But the crux of what you’re talking about, i.e. “physical skills are trainable while mental skills are not”, fall under the banners of “transfer of learning” for cross-domain academic performance, and “malleability of intelligence” for age-related differences in cognitive improvement: e.g. https://files.eric.ed.gov/fulltext/EJ903882.pdf, https://psycnet.apa.org/doi/10.1037/0033-295X.109.1.116.

Plenty of exercise physiology research on coaching format (personal trainer vs. group classes), and strength training adaptations by age that shouldn’t be hard to find at all to cover the physical side.