The father can do everything except breastfeeding, so there’s no reason (except illness) to divide labour on exactly the thing that evolution built the mother to do.
Of course some women can’t breastfeed and they deserve support. But downplaying the benefits of breastfeeding because it may hurt the feelings of some mothers is not the way to go.
It’s disappointing but not surprising that you’re saying that mothers need to go to work in the US. AFAIK in many parts of Europe they take many months off (often 6-12) to spend time with the baby. For some of them, it’s the only time in their life that they’ll get the chance to do that. Work can wait.
Why do mothers need to work in the US in the first 6 months of their baby’s life? Why can’t one of the richest countries in the world pay them to stay at home?
As for parental leave: why not pay men to stay home? Why the presumption that women must be the ones to sacrifice their careers? Because "breastfeeding"? That's a pitiful justification.
I'll say this though - breastfeeding can be a complete mystery for new parents and doctors are often clueless about it. A competent midwife which is familiar with the typical issues is priceless. It's good that there's formula available for those cases where the woman can't breastfeed or the baby is having difficulties and the parent's don't know what to do and can't find competent help.
In the EU, the parents get a number of months which can be split between them. Fathers in Germany for example take a few months off. Because breastfeeding, because moms often want to spend time with their babies and yes, sadly often also because they earn more.
The whole process is as simple as dragging the baby over, taking one breast out and bringing them near to it. The baby will take care of the rest.
Mothers do get sleep, including during the day together with the baby. There are solutions out there for many frequent or rare problems. A good midwife and experienced mothers in the family / circle of friends are priceless.