No, not necessarily.

Trivially, in a monopoly, raising prices infinitely for a product does not maximize profit.

SpaceX has effectively had a monopoly on commercial space launch since it was first able to actually use reusable rockets. Because the innovation of reusing rockets has brought the marginal cost of launching so far down prices will continue to go down.

Right now SpaceX is supply constrained, not demand constrained. All of their launches are booked. As SpaceX's supply increases they will be able to bring launch costs down even further until they hit an equilibrium of monopoly pricing that does maximize profit.