It's really hard to see how impulse would save energy, though. I mean, if the intent is to travel across ten lightyears to get to the next filling station, surely doing it at impulse will use millions of times more energy than doing it at warp? It will last millions of times longer, anyway.
The average speed maintained by the ship probably had nothing to do with the most economical cruising speed - the warp 6.2 guesstimate of the Pathfinder group came from having an empirical look at what one's left with after all the mad dashes at warp 9, all the long trade negotiations and assorted hijinks at friendly ports, all the prisoner release missions and assorted hijinks at hostile ports, all the random hops that took the ship off course, and so forth.
Some tech books tend to claim that the preferred cruising speed of a starship should be significantly lower than the dash speed. However, onscreen evidence is somewhat to the contrary: all the ships frequently travel at or near their maximum speed in order to defeat distances, not merely to defeat a temporary foe such as a pursuing or fleeing enemy vessel. And helmsbabe Stadi in "Caretaker" outright claims that the maximum "sustainable cruise speed" of her ship is warp 9.975, which must be very close to the dash speed of that vessel and in any case much higher than what the ship was ever able to achieve let alone sustain during the series.
Is there any support to the fandom idea that Kirk's ship would have had warp six as a cruising speed and warp eightish-ninish as the top speed? We don't exactly catch Kirk idly cruising in any episode: he likes to get to places as fast as he can, and we hear no mention of increased fuel economy from lower speed. The only thing objectionable about high speed is that it shakes the ship apart; otherwise, Kirk readily goes to warp eight and beyond just to get from A to B.
Picard is the one who allows his ship to putter along at medium speeds at times when en route from A to B. Janeway's approach is more like staying at impulse or random low warp speed when not particularly going anywhere... Which may be a smart tactic for her. Perhaps she has to rethink her course very frequently, due to all sorts of territorial marker beacons that block her way, unexpected subspace swamps, nearby Borg assimilation scenes, the sort of stuff that never would plague somebody with a proper map.
Timo Saloniemi