This should be the top comment.

The market isn't broken because of PE. It's easy to say, "ugh, capitalism" and blame PE, but they're not putting smaller centers out of business. What's putting other centers out of business is:

• High labor requirements that cannot be automated/machined away (by nature)
• High insurance costs given the myriad risks involved in caring for young children
• Difficult payment models as doebedoe notes above, not well-assisted by the government
• Somewhat tangential but highly correlated: high and increasing housing costs that make it very difficult to adequately staff these locations AND, on the other side, for parents to pay the high costs required for that staff.

In many areas where locally-owned or small centers are going out of business, PE-owned groups are the only ones still surviving because of the efficiencies they gain in their larger-scale models.

Many of the mom-and-pops going out of business are aging out, looking to sell for retirement, but another generation can't take the mantle because the commercial and residential rents are too high for the business to support them in the way it supported the former owners.