A lot of other commenters have already touched on the trust factor, but I think that's only one (albeit a key) dimension of the problem. The other is that the

A lot of other commenters have already touched on the trust factor, but I think that's only one (albeit a key) dimension of the problem. The other is that the marketplace dynamics of babysitting are (on average) very different from Uber. Although some people travel, most people use babysitters in their home. Most people use babysitters infrequently. Yes, short notice situations do happen, but most things are planned sufficiently in advance to reach out to a small, trusted group of local/locally available service providers. While the on-demand dimension of a service like this is appealing in those rare instances where you have short notice to find someone and your usual options are booked, this feels intuitively like the minority of situations.