I agree as a former landlord that children can be quite destructive. I also remember the renters that I allowed to have a cat that was evidently fou cats or maybe even when the renters left there were four litter boxes all in a row with as much poop on the outside is on the inside. In other words irresponsible parents of either animals or children are the real problem.
.I know that at one time landlords were able to deny renting to people with children. I can still remember my mother complaining about it when she went to California to be there my dad before he was shipped out in World War II. The following link shows why families with children cannot be denied access to rental property.