A thought experiment: We are designing a transistor and we are designing a material that would give us that perfect transistor - as if we have a "magic container" that has all the elements in Mendeleev table to mix up and provide us with a perfectly mono crystalline material. Only thing left to us is listing parameters we want to have. Would direct bandgap be one of them? Yes, direct bandgap materials are very good - ideal for applications where light involved, but what if the purpose is logic applications?
Also it would be interesting if you would list your top 3 most important qualities for this "perfect" material :)