Taking care of unwanted pets is an expensive task, which no one wants to pay for. Politics are not interested in participating. And finding a forever home for all of them is impossible. Some people recently (November 2021) tried again here in Basel, to get help with the overpopulation of cats (due to owners not castrating their cats which they allow to go outside). Mainly they want them to change the law, to make it mandatory to castrate your cat if it has access to the outside.
It's hard to hear, that people bring unwanted pets to the zoo, to throw them away. A year ago I adopted Fawkes, an unwanted cat, who should have been euthanized if his previous owner had her way. I just can't understand those people.
But I never heard that this is a thing here in Switzerland. Bringing your spare pets to the zoo? And it doesn't make sense to me - I mean, what if the pet is sick and the previous owner doesn't know about it?