As for the theory working better in flat spaces, it is the full theory, with supersymmetry, strings and all that. Point is that the product space of minkowsky times extra dimensions is not granted to be a solution of the equations of full (with extra dimensions) general relativity. In some cases, you can make it to be a solution, but with a cosmological constant. It is up to you to discuss how troublesome the situation is. Nowadays, the only extant argument against a cosmological constant in the 11D Lagrangian is that it breaks supersymmetry.
