I admit, I got my original pair as disposal units back when I was actively breeding about 30 species of freshwater fish. There is always the necessity to cull some of the spawn with fish, and I did not have the stomach to do it myself. Axolotls were the answer.
Problem was the little buggers grew on me. Their goofy looking "grins" and attentive habits when feeding became like a lava lamp to me. I just couldn't help watching them more than the fish. Once my health took a bad turn, I had to give up fish breeding. The axolotls stayed though.
Pretty soon, I was actively breeding them! That led to other amphibians and reptiles...
Even my wife, squeamish about most critters fell in love with them. To this day, she often reminisces about the original pair and how they would actively swim to the surface of the tank by the desk to be fed.
I think for many people, a quiet, easy to care for, hypoallergenic pet is very attractive. I know in many places, they are the only caudate that is legal to keep. I think the allure of what is really a very uncommon pet attracts a lot of keepers too.