If the idea here is that more diverse companies can pay lower wages and benefit that way then it may have something to it but it's hard to see that as the market "solving the problem."
Of course we assume, in this thought experiment, that all the other things Company Bigot could do to become more competitive (invest in more employee training, better infrastructure, etc) are also available to Company Diversity. This isn't always the case. Maybe Company Diversity's hiring practices have alienated it from potential suppliers or clients who prefer Company Bigot's views.
Specifically I'm thinking of Japan, where (apparently; source: this site) the cultural emphasis on the salaryman paradigm means that hiring from the significant pool of contract labor can hurt your company image as far as working with the established corporations is concerned.