The Mozilla Foundation's legally-binding mission statement is therefore also effectively enforced for the Corporation. The Foundation could throw out the CEO of the Corporation and in general gets to decide what happens in the Corporation, which they're legally bound to tell to follow the Foundation's mission statement, i.e. making the web a healthier place, improving privacy etc.
As a result, the only profit-motive that exists in the Corporation is that the employees want to keep their job.
A small correction: if I recall correctly, the Corporation is legally allowed to give some money to the Foundation, and it does so. But the allowed amount is quite small -- maybe a couple a million a year? I don't remember exactly -- and only a tiny fraction of the Corporation's profits.