First, the market for child care that we face as individuals is one largely of our chosing. In a macro sense, we make choices to live close or far from family, to be in a close knit community or not, etc.
In a micro sense, are we comfortable with an off the books nanny coming to the house, or dropping the kids off at some illegal community grandma's house every day?
In NYC, no poor person deals with the "$150 just to get on the waiting list" type of child care. The people who engage with that are people who chose to raise kids in the city and want a certain type of "formal" daycare. These people also make enough that the cost/benefit obviously makes sense to them.
These are also people who would never use a broker because they don't consider daycare a fungible good. It's not like sourcing a trading venue for your sovereign bonds - by the time you are playing this game, you have very specific expectations about the philosophy of education, setting, religious context, etc.
Meanwhile, the poor people already have grandma living in the house, she gets SSI so the daycare is subsidized. And if there's no grandma in your house, there's one next door who'll keep an eye on your kid too for a couple of bucks an hour.
This is a very interesting example of where religious communities outperform the secular. For example in NYC is not uncommon to meet Orthodox Jews with 10+ kids. The secular can't relate to what it's like to have to deal with child care for 10 kids. But in those communities, it's routine - your family and neighbors help you out and you get through it. The fact that as seculars we fail to achieve that for ourselves is an interesting signal in my opinion.