My analysis of this: I think you are blurring the lines between interior designer and project manager. You are asking the interior designer to run the entire renovation. That may be totally feasible for some interior designers, but to quote this "A contractor is better at building than picking materials" could also be said about interior designers. They could be great at picking materials, but do they know when electrical, plumbing and hvac needs replacement? A shady contractor could potentially pick up on someone lacking knowledge and take advantage of them, thus costing you money.
I would look for a project manager and hire a designer on a job to job basis (let the project manager deal with them). When I was flipping in South Jersey I was doing sub 200k builders grade flips so I didnt need to use a designer. But when I think "designer" I think picking materials and finishes, not managing the contractor. Just my $.02.