Why is it a "critical advantage" to measure how much the baby eats? Babies need to eat when they're hungry and they stop when their stomach is full.
For a minority of parents, the child will be "failure to thrive" and for that you will need to measure intake, but the child will also be on special high calorie formula anyway. So at this point the advantage is irrelevant.
"Measuring" is a really stupid reason to deny your kid the other benefits of breast feeding. However, there are many viable reasons not to breastfeed, such as it's just not working, or the mother needs to work/have a life, or it's painful, etc.
Politics, nutrition and parenting are all conversations I attempt to avoid, and this combines 2 of 3 topics. :/
That said, it was pretty obvious that she was getting enough, it was just mildly uncomfortable not knowing how much.