I think there should be a middle ground…
I think the ACT has that middle ground. A particular animal can be refused permission on reasonable grounds and reasonable conditions can be imposed. What you can’t do in the ACT is ban pets outright. It would be hard to find reasonable grounds to ban a couple of goldfish but there could be reasonable grounds to refuse such a quantity of fish that an aquarium containing many tonnes of water would be required, possibly overloading the building structure. Similarly, a cat confined to the unit area would be hard to reasonably refuse but an elephant might be.