This is a pretty good distillation of the math. Child care has often been done on the backs of underpaid lower-class workers. Unlike most businesses, childcare doesn't scale well at all, and it's very hard to make the math work to pay the staff a living wage without it being prohibitively expensive.

Even in the example given, the $22.50/hour rate is just the break-even rate with child-care workers at the minimum wage. If you push them up to a living wage of 75k/yr, the listed cost doubles. Add again people wanting child care costs to not just be break-even but to make working feel worth it, and it probably doubles again.

It's just a very hard business with difficult scaling. It gets better after age 2, when you can increase your student/staff ratios, for what that's worth.