A related question is "why does Kirk default to Warp 1 after crises, even when it would make sense to go as quickly as possibe, like at the end of "The Galileo Seven" (after the crewmembers are back on board).
hmmm.
....Well, in that particular instance, a shuttle exploring the four star systems within the miniquasar zone and therefore supposedly moving at maximum warp had gotten into big trouble. Perhaps Kirk felt that flooring the mothership's warp engines might result in a similar magnetic catapult effect, and tiptoeing out of Murasaki was the sensible alternative?
Timo Saloniemi
And of course for some reason there might not be much speed improvement in going to high warp speeds near a habitable planet. Possibly going to a higher warp factor would only give a slight speed increase within a star system compared to farther out.
Some people theorize, for example, that starships travel much slower at warp speeds when they are within strong gravity fields near a star. If, repeat if, that is the case, going from warp factor one to warp factor two, or from warp factor two to warp factor three while deep within a star system might result in a slight speed increase for a large increase in the amount of energy used by the engines.
I note that the amount of energy received by a planet from its star and the intensity of the gravitational field of its star at the distance where the planet orbits do not have a one to one relationship.
All class M planets habitable for humans with oxygen-nitrogen atmospheres and temperatures fairly comfortable for humans will receive approximately the same amount of radiation and light from heir stars, within fairly narrow limits. And of course the amount of radiation a planet receives from its star, and the intensity of the gravitational field of the star where the planet orbits, will both vary with the mass of the star. The more massive the star, the greater the radiation received by the planet and the farther from the star it has to orbit to have a habitable temperature, and the more intenser the gravity of the star will be at a specific distance.
But the gravitational attraction of stars and their luminosity will not vary with mass at the same rate. A small change in stellar mass will produce a small change in stellar gravity and a much larger change in stellar luminosity.
A star 1.0, or 1.5, times as massive as the Sun will be much more than 1.1, or 1.5, times as luminous as the Sun. A star 0.9, or 0.5, times as massive as the Sun will be much less than 0.9, or 0.5, times as luminous as the Sun. Planets in the circumstellar habitable zones of stars more massive than the Sun will orbit where the star's gravity is less intense than the Sun's gravity at Earth's orbit. Planets in the circumstellar habitable zones of stars less luminous than the Sun will orbit where the star's gravity is more intense than the Sun's gravity at Earth's orbit.
And of course the mass distribution of stars is such that less massive stars are more common than more massive stars. So in a realistic space opera most of the habitable planets visited would be orbiting stars less massive than the Sun and thus within more intense stellar gravity fields than Earth is. So if strong gravity fields slow down warp drive, it would little use to use higher warp factors near most habitable planets.
Of course in
Star Trek habitable planets are found orbiting many stars known to be of types where it is considered impossible for habitable planets to naturally develop. Thus any habitable planets found orbiting those stars should have been brought to those stars from other systems by super advanced civilizations and/or been terraformed tby advanced civilizations o become habitable.
And the theories to explain distance, speed, and time problems in
Star Trek include a theory that a common method of rapid interstellar travel in
Star Trek is the use of a natural or artificial system of gateways or stargates providing instant travel between star systems. And possibly impulse speeds or warp factor one or warp factor two might be quite adequate to travel between the mouths of those gateways or stargates that might be only a billion miles or something apart within a star system. High warp speeds might only be necessary when traveling though all of the interstellar space between two different star systems instead of using the shortcuts provided by those gateways.
in my post number 77 at:
https://www.trekbbs.com/threads/tos-chronology.304218/page-4 I mention that theory with especially relevance to "the Galileo 7".