This opens the door to exploring phenomena like consciousness, freewill, and other such concepts and either tries to make allowances for them into our materialistic theories or to come up with an argument of why we can't.
Eliminative materialism is in keeping with the overall philosophy of empiricism.
What really is relevant is what we actually see or experience. We don't see anything that could lend itself to something like consciousness. All we really see is behavior, and the only reason why we are even interested in consciousness at all is because of introspective inquires of our own mental processes. This is what lead Descartes into thinking that there was non-material thinking stuff in the first place. However, there's a problem here.