The way that impulse speed has been depicted in Trek is that it only works when "on". In ST3 for instance, the Excelsior coasts to a stop once her engines are disabled.Why not do constant thrust? It's faster, and speed is survival. Or, more exactly, travel time is inversely proportional to survival.
The ship wasn't supposed to be short on fuel for impulse travel in "Where No Man"; at most, her impulse engines were two steps away from blowing up, even after Kelso's well-advised repair. It was the main drive that was out of oomph and awaiting refreshments from Delta Vega. So accelerating all the way would make the best sense.
Or accelerating halfway and then decelerating the other half. But Trek ships never do that. There instead exists some sort of a magical braking system that can perform negative acceleration a thousand times better than the impulse engines can do positive acceleration. Perhaps a drag chute you can deploy into subspace or something? Real space is symmetric as regards acceleration and deceleration; a fixed frame of reference in the form of subspace would nicely break that symmetry and make braking easier than accelerating.
Timo Saloniemi
However, this is consistent with some sort of mass-reduction field being in effect (such as in DS9's pilot episode) which would be entirely necessary given Enterprise's tiny engines, small fuel volume and massive speeds often achieved with the Impulse Engines. Bereft of a MRF, the Impulse Engines would be barely better than manoeuvring thrusters.
In WNMHGB the ship was severely damaged with likely numerous systems barely functioning. There might have been just enough juice in the mass-reduction tech to get the ship to the planet, after which the crew would have been entirely dependent on those dinky little Impulse Engines to blast out of orbit (which Kirk surmised would not have been enough)