Noted, thanks. A quick internet search seems to confirm your point, but I'm not totally convinced yet. I note here:

"the actual causes of low milk supply at the molecular level inside a breast’s epithelial tissue are still unknown...

Interestingly, the change in breast size (breast volume) from pre-pregnancy to lactation can be an indicator of how well the breast performs during lactation"

milkgenomics.org

I wonder whether there is an indirect link, and not all fat is the same — so maybe the breast grows specialised fat to feed the milk-producing epithelial cells, which normal fat can't do (hence obese women with big breasts don't make more milk).

Also the research is probably done on typical western women with only one or two babies to feed. Being able to feed many more hungry babies in a collective cave tribe might be different.