You're making an assumption that the cat, or whatever type of pet, is not happier than they would be being tied up in a back yard forgotten about most of the time. Or, living on scraps in a dumpster.

Is that normal? Or a better life in your opinion?

Seems to me like being the pet of a "scary" single woman means having a long, comfortable, life. Clearly, better than a lot of the "normal" alternatives.