Indeed, we have pretty explicit evidence that high warp near stars is a crawling speed. We actually see
how incredibly slow "warp 8" becomes when you do it right next to the Sun in ST4:TVH. Similarly, extreme warp sustained for hours is barely enough to compensate for two months of travel time of a necessarily sublight asteroid moving the opposite way in TOS "Paradise Syndrome". And for some reason, high warp was not an option in the desperate chase inside Sol system in TNG "Best of Both Worlds II". For some reason, the E-D only moved at about twice the speed of light after her brief stop somewhere near Saturn or Jupiter.
One might thus conversely argue that when a starship gets very far away from the nearest star, warp speeds suddenly become much faster than in the average interstellar environment.