particularly that they measure the variance of a factor rather than its absolute importance (and hence you get results like variation in nutrition being almost invisible as an explanation for variation in height)

Excellent point, which deserves some elaboration. Suppose that very high doses of vitamin K dramatically increase height, but that almost nobody is experimenting with such doses. Then a heritability study will find that environment contributes little to the variation in height - but that's usually not what we want to know. What we want to know is more likely something like, what steps can I take to have tall children?