Black Hole Drives
If you have an interstellar civilization, presumably travel between stars is somewhat fast (i.e., weeks to months, rather than decades to centuries). None of the technologies we have today are remotely suitable for such interstellar travel. Nor have you stated how hard-science you want your drive technology to be. But if you want somewhat realistic physics, then your best bet is a "black hole drive".
A black hole gives you near-perfect conversion of matter to energy, if you are able to harness it. You literally just let matter fall into the BH, and as it does, tidal forces pull it apart and release gamma rays and other energy, which is how we "see" BHs today. Obviously, if your BH is too big, then it is hard to move, making it a terrible ship drive. And if it's too small, then it will evaporate too quickly, turning into a massive bomb that will annihilate your ship (and a bunch of stuff around it for quite a distance!). So it turns out that there's a "Goldilocks" size which gives you decent power but portable mass.
The problem with a black hole drive is that the BH needs to be fairly small to be reasonably movable. And the smaller a BH is, the faster it evaporates. As mentioned earlier, you don't want that to happen! So you need to constantly feed it mass, to maintain its size within an ideal range. This means you need a steady source of "fuel". Fortunately, they aren't picky about what you feed them, but there is no way to "turn it off."
Your hand-wavium works if you make the drives + fuel load only big enough to travel between "adjacent" stars. After all, your average velocity will depend on your mass and thrust, and at some point, adding more fuel will increase the trip time to unacceptable levels. Thus, the ships need to stop at planetary systems simply to bring more fuel mass onboard.
Although a black hole doesn't care what you toss into it, how you harness its energy matters a great deal. Also, the BH itself is microscopic (much smaller than an atomic nucleus), so just directing fuel into it may be a non-trivial matter all by itself (pun intended). One problem is that Hawking radiation from a subatomic black hole (SBH) is expected to be hot...very hot...like, gamma-ray hot. And gamma rays are so energetic they are not easy to harness. Just making an adequate shield so that the crew are not fried is a serious engineering problem. However, it may be possible to create a "gamma scintillator" which "down-converts" the gamma photons to UV range or lower. However, gamma rays are so energetic that they are going to eventually degrade/destroy your shielding anyway via photodisintegration and photofission.
So, there's two possibilities for requiring special refueling facilities: 1) The fuel itself needs to have certain properties amenable to focusing and control, and 2) the gamma shield probably needs to be replaced at regular intervals. Since 2) strongly favors heavy (high Z) elements, this is exactly the kind of thing you would want to visit a rocky planet for. Since your ship needs to be as small and light as possible to maximize useful cargo mass, it can't carry a full shield manufacturing facility that can just drop onto a deserted planet and manufacture new shielding for you.
Both your civilizations may prefer living planets if they are predicated on the idea that life will spontaneously form on any planet with the basic necessary ingredients: liquid water, thick atmosphere, magnetosphere, abundant carbon, nitrogen, iron, etc. Thus, a planet with no life is lacking one or more of the essentials, and becomes unattractive for colonization, even for just a refueling station.
You can hand-wave this a bit more if you argue that the shield manufacturing process requires nano-machining which is best done organically, by engineered bacteria/protista, which, in turn, requires massive quantities of water to operate at scale. So even though it may be technologically possible to build a refueling station on a dead world, it is economically infeasible.