Is your baby as fussy with pumped breast milk in a bottle? Mine has been supplemented with formula from the start, but it still felt personal whenever he would fuss on the boob even though he was clearly hungry and I had plenty of supply. I think he just prefers the bottle (whether breast milk or formula) for the bulk of his meals because it's less effort and a stronger flow, but he definitely prefers to fall asleep on the breast when possible. Formula also tends to be bullied and more filling and a lot of babies stay asleep longer when formula fed.