They aren't THAT much easier. At home defense distances, the spread of buckshot will be about the size of a human fist. While that is certainly a larger margin for error than a single 9mm or 45 projectile, you still have to be pretty competent and accurate. The biggest advantage is that you have a longer sight radius than a handgun and as such it is much easier to aim (yes, you should try to aim in a home defense situation even if you end up primarily point shooting), well and the extra power from the number of pellets. The first one, however, is an advantage they share with rifles. Your point about cost is valid too if someone is on a budget.
It sounds crazy, but in many cases rifles (specifically those chambered in 5.56/.223) make a better home defense weapon than a shotgun for several reasons. Up front, the biggest disadvantage to rifles is how loud the blast is indoors. Any gun is loud, but rifles even more. That aside though, a semi auto rifle has a higher capacity, lower recoil, less manual manipulation neccessary, and less penetration through building materials. That last one sounds counterintuitive, but due to the speed and light weight of 223 projectiles, they tend to yaw and tumble going through building material and actually penetrate less. If you use frangible ammo, it's an even more pronounced reduction in penetration. People also have a tendency to short stroke pump shotguns under stress, especially if they aren't experienced, a problem you don't have to worry about in a semi auto rifle. Pop a light and a red dot on top of a semi auto rifle and you have a great home defense weapon.
Never, and I mean never, should you shoot someone in the leg in a home defense situation. Doing so increases the chance of the projectile(s) missing your target and harming or killing someone else in the dwelling. You want to aim center mass to A) Increase your chances of a central nervous system incapacitation and B) Decrease your chance of pass through that you can't control. You should not be shooting at someone unless you are willing to end their life. If you aren't willing to do that, you shouldn't be shooting. The femoral artery is in the leg, and you stand a good chance of killing them anyway if your intent is to injure.
I apologize for the wall of text. Home/self defense and firearms are an important thing to me in no small part due to my profession. If anyone is seriously looking at options and would like help or insight, I'll gladly do what I can. I'm no professional, but I'm an enthusiastic enough amateur that I've learned a thing or two.