Pumping and storing breast milk is extremely common. You can absolutely give your child breast milk and work, and I know many professionals who do.
Just handwaving "but pumps!" really undermines how much effort this takes for women.
Still, the approach presumably should be more, not less, support for women who want (need?) to try this?
Of course none of this stuff is critical, but I think for most people, the ideal scenario really is breastfeeding, straight from the breast -- and it's a shame that's so hard for so many to do in our society.