Love this question! The first thing that comes to mind, is, because: a) I'm a romantic, and b) because I can. I love single-shot rifles. Mostly don't need but one well-placed shot, though not always possible. But then, managing a second shot w/a single gun is not hard. I've been hunting w/a TC Encore for years, and love it (my go-to gun this year). Someday I'll break down and get a Hubertus or some such. On the practical side, as many have mentioned in this post, the versatility of having a shotgun (one or two barrels) and a rifle, all in the same package is extremely handy. I lived in Florida, in the Ocala area, and everyone there hunts with dogs chasing deer. They carry two guns - a shotgun and a rifle. Obviously, one is for up close shots and the other long shots. Problem is, you invariably have the wrong gun in your hands. With a combo (or a drilling) this isn't a problem at all! That's the beauty of it. Now, living in Northeast PA, sometimes deer and fall turkey seasons overlap. I would not risk spooking a deer shooting a squirrel, but for a Turkey? You bet. And, if an animal bolts a shotgun is better for a close running shot than a rifle. A combo/drilling gives you a CHOICE. I love the fact that combo/drillings are break-apart guns (including taking off/putting back on scopes). Compact. Great for travel. Next, I would say, is the balance and familiarity factor. It's the same gun all the time. You get used to it, the fit, the feel, the balance, and trigger management. You are much more apt to shoot it better. Being a romantic is impractical. Not in this case!
Pierre