I agree that assumption is the wrong word. But do you have examples of monopolies that didn't take the profits and control the pricing of the markets they control?

No, a monopoly is controlling a market to the point where competition is restricted via controlling supply or other means. A company can have 100% market share and not be a monopoly (which is always what happens when a new market emerges).

A better example would be you own 75%+ of the cinemas but revenue wise you only control 50% of it. And in that case I think it's fair to do it. If they would force Apple out that would be a problem, but instead they even give you the basis for your own cinema for free (in contrast to Apple).

Edit:perfect->problem