No, these are not necessarily examples of market failure. I'd suggest reading up on the concept. A large and long lived discrepancy between the price of somethi

No, these are not necessarily examples of market failure. I'd suggest reading up on the concept. A large and long lived discrepancy between the price of something and its cost of production might be an example of market failure, perhaps due to a monopoly. It might also be due to government failure (excessive regulation, subsidies, tax policies, etc.). A temporary discrepancy is not market failure at all, it's how markets work. In the case of child care it is not even clear this situation exists, most of the reasons you listed earlier were reasons why it is expensive to supply child care and not evidence of excess profits.