Does the price level in a competitive market have to be at the intersection of the Average Cost curve and the Marginal Cost curve?
One of the assumptions of perfect competition is that firms are price takers. Ultimately price is determined by the quantity of goods supplied, and with perfect competition, there are infinite (or an arbitrarily large) number of firms, so a firm that changes their price by itself will simply have no business, since there are cheaper places to buy from. The quantity supplied will also not change, and will leave the prices unchanged.

So what happens if all infinite of these firms tried to unilaterally raise their prices to the same level? This is maybe in some cases a Nash equilibrium, but not a coalition-proof Nash equilibrium. So firms could also unilaterally deviate from the higher price to take the whole market between themselves.



If price (marginal benefit), was suppose, forced to be higher, so that you moved along the marginal cost curve where MC $\neq$ ATC, then the supply curve would shift, because the optimal production quantity would increase for all firms at this price control. And the market would then not clear.