there’s a great planet money podcast that covers this

It turns out childcare is just a very labor intensive sector due to the amount of adults needed to watch the kids. This means that most of the costs for daycare are already labor:

In fast food, labor is 25% of the total costs. Estimates for day care - it’s, like, more than 70% of total costs.

Given that labor is already a disproportionate amount of the costs, raising salaries a little has a large effect on the increased cost that parents would have to pay.