It depends on the species. It’s one thing to neuter a giraffe but if you have a flock of peacocks or a colony of 40 bats you are probably not going to do surgery on all of them, it’s also very hard on some of the smaller animals. Making an effort to keep only females or males would be an option for some species but not all, as they won’t always show their full range of behaviour.

The article does point out a lot of it is small rodents, but also things like tadpoles or fish. It can be extremely difficult to control their breeding (or even identify their sex without cutting them open) yet detrimental to their welfare to allow them to be overstocked. The real solution here is probably not invasive birth control techniques (even restraining an animal to pill them can be very taxing), it is more effort to share surplus animals with other zoos, wildlife refuges, wild release etc with particular attention to those that are prone to being culled. But again, transport is a huge stressor for animals, so you have to consider that the potential benefit to them should be more than the risk of worse welfare.