I don't think the brain relies on a spin cycle like a washing machine, but maybe it's not so far fetched. Walking and being generally active helps the body "pump" lymph.
My go-to analogy is a movie theater. Once in a while you have to break out the firehouse and wash down all the accumulated popcorn, gummy bears, dried-up soda pop, and tracked-in dirt. And no, it cannot all be recycled to make new movietime snacks.