Hmm...I've never used a Nanny for a infant. So that is rather strange. I know for toddlers, the nanny does indeed only need to do is cook and can ask the Nanny for things if needed. Since our little ones can pretty much do everything else on their own. However maybe EA figured that that we wouldn't need a Nanny for infants and assumed we'd put them in daycare, compared to the toddlers since most might want to continue working on skills while mom and dad are gone.
This is interesting, I might try this for the next generation of future infant sims in my game.