I've got two chihuahuas. It was because of how they look, but when I started to properly research the breed, I was delighted to find out how healthy, long lived, and robust they can be if from a reputable breeder. I got one first, after six months of negotiations, with several, very lovely breeders. A year later I got her little sister, from the next litter.
We adore them. They're totally delightful little dogs. They are exercised with our elderly rescue staffie, and tank about like dogs should. They are super cute, really lovely with our ten year old dts, and as a pp said, their poos are tiny! They are a joy for us. I'd be really surprised to ever see rescue centres full of chihuahuas.
Sadly there will always be wankers who breed animals that they shouldn't, and idiots who buy pets they shouldn't, but I don't think it's fair to generalise.