This has been done. Women seem to have certain health benefits that stop after menopause. Reading about it was the first time I wondered whether blood letting made sense.
God, this is so ignorant, the hormonal changes (loss of estrogen) are the cause of increased risks for heart disease and osteoporosis and changes in metabolism post-menopause. Nothing to do with not physically losing blood, FFS.
There are likely multiple causal factors behind the health differences. Hormonal changes are one piece of the puzzle but so far no one has conclusively proved that physically losing blood has zero effect. The research just hasn't been done yet so we can't definitively say one way or the other.