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Public parks are not personal spaces to populate and use as you see fit. They are also public.

The rhetoric about free roaming cats is also only partly informed.

Firstly it is recognised that indoor cats are much more likely suffer from health issues relating to anxiety and depression. The why is not studied particularly well but it likely stems from completely destroying their ability to socialise, and restricting their roaming area (which for cats is very large). In many places keeping cats indoors is considered cruel.

Secondly, the effect of cats on the environment is completely dependent on where you are. This is because the danger of a cat comes from their predatory nature and most places - especially after the spread of humans - are lacking in active predators. Obviously there are areas where the risk posed by a non selective predator is very high; areas with endangered populations may want to encourage people not to gave cats or to regularly clip claws.

Again, as it turns out the world is a wonderfully diverse place on which homogenous rules are a bad fit.