^Exactly. "Impulse engine" is simply a fancy name for "rocket." There was at least one episode where Kirk actually referred to them as rockets. But as I said, the more massive a ship gets, the less effective rockets are at accelerating it, because of inertia. A ship the size of the Enterprise
-D would take forever to get up to speed or to turn onto a new heading. So once ships got that big, it became necessary to supplement
the impulse engines -- i.e. the fusion rockets -- with a mass reduction field, so that the ship would become effectively light enough that the engines could accelerate it more easily.
Granted, there's no reason they couldn't use warp engines for sublight propulsion. In fact, the real-life theoretical warp equation developed by Miguel Alcubierre, and refined by other theorists since, might actually be more feasible to use at sublight than faster than light, due to the enormous practical difficulties with the latter. But you'd still need some kind of secondary propulsion system based on conventional thrust. An Alcubierre-type warp field could only take you in a preferred direction if you had already thrust your ship in that direction before you engaged it. So it stands to reason that impulse drive might have advantages for sublight propulsion that warp drive wouldn't. You could
use warp drive to maneuver at impulse, but it's not the best thing for that particular job.