And if he was so close that it would only take a day or two, why didn't the Enterprise just take three seconds and warp him over there?
There are dozens of episodes where the heroes take a shuttle to visit a civilized starport, while the ship isn't on Red Alert and could just as well go orbit the planet and beam down the heroes.
On the other hand, there are episodes where our heroes drop their starship to impulse well before going into a star system, even though they are
on Red Alert and in extreme hurry. And there are even instances when our heroes claim that going to warp within a star system would be a problem, even though some 99% of cases feature effortless insystem warping.
And then there are episodes where high warp within a star system amounts to crawling speed...
We might decide that certain star systems, perhaps during bouts of adverse subspace weather, make it very difficult for a starship to ply a warp path to the target world, and going by warp won't be any faster than going by impulse. In such conditions, there's no point in using the ship, as she has to waste time both going in and
getting out. Better to drop off the required heroes in a shuttle, with or without warp drive, and use that shuttle to sail in at impulse speeds.