Why, yes. I'm not a zoologist, but I know giving a replacement milk is the best solution when the mother either is absent for whatever reason, cannot produce milk, or cannot produce enough quality milk. This is why we have milk for infant cats and dogs, actually. Otherwise, the animal would die. There is a similar nutrition for birds (as they don't produce milk) and it is common for folks to buy pigmy goats as an infant and bottle feed them.
Why do humans think they're any different?
We don't. Replacement breast milk saved lives, and these sorts of issues were the original use of infant formula. When applied to current society, it still saves lives and helps to keep folks from financial ruin because some countries (like the US) don't really give mothers time off work to properly breast feed, and it is usually difficult to pump milk at work. At some point while pumping, people usually have to supplement formula as well. As a side note, I was one of the babies that would have died without a wet nurse, as my mother had gall bladder surgery before I was 6 weeks old (fairly major surgery in '78) and could not breast feed.