On the few (read: one) occasions on which we've been entrusted with the life of another's child we've never thought "Hey, this is so enjoyable, I would pay to do it on a tiny screen." Babies are noisy, and they smell like milk sick and (often) doody. In fact, "it's like a job that you pay to do" is rarely a recipe for gaming success. The notable exception here is Burgertime, and only because being chased by giant eggs and living to tell about it is the most alive you can feel without the use of crystal meth.
Exhibit 7,324 that no one asks us before they decide to make stuff: Casual PC game Babysitting Mania is coming to the DS. You can play it for free right now on the PC, if you want. Or, you could take the precious life-seconds you would spend doing that, put them in a rocket, and shoot it into the sun. The choice is yours.