On top of respecting user privacy, this feature also reduces costs for Apple because the company does not have to pay the bill for servers to process the hundreds of millions of images that their customers produce.
On a much smaller scale, it is now possible to run some deep learning models in the browser. This is especially useful for demos—by running the models on the user's computer, you can avoid paying for a costly GPU-enabled server to run inference at scale. Moreover, there will not be any overloading issues because the more users that access the page, the more computing power that is available.