The “warp shell allows one to modify the state of spacetime inside it…the time in the inner region may go faster or slower than it would go without the shell” [1]. Being “internally moving shells of normal or exotic matter,” these warp shells “do not have any natural way of changing their velocities. They are just like any other types of inertially moving objects. Similarly, just like for any other massive object, achieving a certain velocity for a warp drive requires an externally applied force or, more practically, some form of propulsion.”
Subliminal warp drives let a timelike passenger compress the subjective experience of the journey. It doesn’t change the journey’s propulsion requirements. Think: cryosleep benefits from science fiction, not Star Trek-esque warp.