You are exactly correct in that within a couple/few yards you get one large hole. The difference comes with the terminal ballistics. Those 9, 12 or 15 00/000 pellets will fan out upon entry into the animal, each perusing modestly different paths, and cause more damage than a single slug or bullet path. I’ve never necropsies a shot cat but I base this on what I have seen in human torsos in my capacity as a forensic pathologist and in boar hogs as a hunter. With the advent of tungsten buck shot, even the valid concern regarding the penetration (as opposed to a bullet or slug) of the individual shot balls has been obviated.I feel some of the desire to use a shotgun comes from the idea that you have a wider margin of error because of the spread of the pellets at the distance of expected use, that is the same thinking that people use to justify a shotgun in a close quarters scenario for defense. A shotgun at 10 feet, or whatever range you envision your encounter with a cat charge, is the same as a rifle shot. They make one hole or something VERY close to one hole. You still have to have precision in your shooting, and after 1000s of rounds of shotgun practice, I am still less precise with a shotgun than a rifle.
I have never had to make a shot on a charging cat, and I hope that trend continues for the rest of my life, but if it doesn't, I want to have a rifle with a red dot.