For me (a strictly visual observer), I think it's mostly a matter of ease of use (for the ways in which I prefer to use a telescope) combined with ease of maintaining and caring for the instruments. I've been able to keep my refractor optics in pristine condition. Each and every time I take out my oldest refractor its optics are every bit as clean and pristine as they were upon first opening the straight-from-the-manufacturer box some 28 years ago. And as many are aware, cleaner optics translate to less scattered light and higher contrast views.
It doesn't bother me to stick with smaller aperture, refractive telescopes. They're fully capable of showing me more than I've ever desired to see.
Mostly, my refractors are achromats; but I also have refractors that occupy each end of the quality scale -- a singlet refractor at one end and an apochromat at the other end. I enjoy each refractor type for its own unique set of strengths and weaknesses. I enjoy seeing celestial bodies much the same as some of history's visual refractor observers saw the same objects (It helps that I enjoy similar sky conditions )
At the smallest of apertures, the refractor is king. At typical amateur refractor apertures, aperture for aperture, the refractor is the most efficient design for raw light-grasp. But, of course, image sharpness and contrast will vary a bit depending on the specific refractor. At the high end (an apochromat of the highest quality), aperture for aperture, the refractor will provide sharper and higher contrast views than any other telescope type.
When one considers what a really small refractor is capable of, one needn't go very large in order to get some truly spectacular views:
For example, a 1-inch aperture used for lunar observation:
and, under a seriously dark sky, a 1-inch aperture for deep sky observation:
Of course, lunar details (in a 1-inch refractor) are much smaller than those shown in the first sketch; and deep sky views are much fainter than what is shown in that second sketch. But, with experience, one learns to pick out fine detail even when the view in the eyepiece is quite small; and one also learns to pick out faint details in deep sky objects. It's worth noting that as far as the details that appear in the above sketches go, those sketches are accurate and true to what was seen visually.
Imagine how much more could be seen with double the aperture, for example, with the below 2-inch refractor:
Yet, I have the option of setting up even larger 3.14-inch, 5.1-inch, and 6-inch refractors -- up to six times the aperture that was used for the above observations/sketches.
So really, refractors can provide me with all the aperture that I could ever desire. But I guess I needed to acquire and use 10-inch and a 12-inch Newtonians before I came to that realization. Anyway, those larger telescopes haven't been used in several years. Their advantages (and yes, they do have advantages) are outweighed (for me) by their disadvantages.
For me, I think it mostly boils down to ease and suitability of use and ease of care/maintenance; but it doesn't hurt that refractors can also perfom .