Why would a natural monopoly lose money when MC=P, but a competitive firm would get positive accounting profit? I assume that the natural monopoly is required by law to have maximum price=MC. According to this video such regulation would require constant subsidies for monopoly, because otherwise it would go bankrupt:

https://www.coursera.org/learn/microeconomics-part2/lecture/VWpuW/3-1-6-natural-monopoly-regulation-though-marginal-cost-pricing

The monopoly losses money because P &lt; ATC, while for a competitive firm P > ATC.  Somehow it seems that a competitive firm would have lower ATC than a monopoly. I don't understand why.
I found the answer in "Intermediate Microeconomics" by N. Gregory Mankiw.


  When a firm’s average-total-cost curve continually
  declines, the firm has what is called a natural monop-
  oly. In this case, when production is divided among
  more firms, each firm produces less, and average total
  cost rises. As a result, a single firm can produce any
  given amount at the smallest cost.


...


  By definition, natural
  monopolies have declining average total cost [due to economies of scale, I suppose]. As we first discussed in Chapter 13, when average total cost is declining, marginal cost is less than average total cost. This situation is illustrated in Figure 10, which shows a firm with a large fixed cost and then constant marginal cost thereafter. If regulators were to set price equal to marginal cost, that price must be less than the firm’s average total cost, and the firm would lose money. Instead of charging such a low price, the monopoly firm would just exit the industry.


From other book:


  If demand is large relative to the minimum efficient scale, a competitive market is likely to result. If it is small, a monopolistic industry structure is possible.


Of course there must be the point where MC=ATC, but if the demand will ever become big enough to go beyond this point, then it will probably mean that our natural monopoly isn't natural anymore, that it makes sense to (re)introduce competition because now we have diseconomies of scale. Although it can be exactly MC=ATC, but it will be just coincidence and as such is unlikely.