Yes, they do, it’s for PROTEIN so the cow can make enough fatty milk that it’s good for the calf and for butter, and so the cow stays healthy in the process. Do you have any idea how much extra protein and fat a pregnant and nursing female of any mammalian species needs in order to stay healthy?
Even the local dairy farms around me, that keep their cows on grass as much as they can, supplement feed.
Here’s an actual farmer talking about it if you want to hear from someone in the industry.
For more cow related content, here’s him on how the beef cattle industry are largely a bunch of whiny bastards who want to have their cake and eat it too, if you want to have something that is actually worth getting mad about.
An addendum, just for funsies: him talking about the silliest chicken myth he’s ever heard (and he’s heard a lot).