Sorry but its complete rubbish to say its safer on the Users equipment! Of course its not, it gives the potential for modification and access to over 1,000,000,000 users unique identifiers plus anything else that the software was modified for.
On the server it can only serve the general function at present NeuralHash, which as Apple suggest is designed to be anonymous anyway.
It doesn't even make financial or ecological sense to have it on 1,000,000,000+ devices, as its that number of downloads, that number of processing time, electricity etc., whereas installing it at the cloud end requires 1 piece of software.
It would be the same neuralHash tools so anyone suggesting it conveys more privacy on your own device just doesn't understand Apple software nor the fact that Systems Integration protection, stops other companies from changing system files, whereas Apple bypasses that, as authors.
When costs are greater to put on individual hardware and they are, then its there for a reason, and I do not believe it should be on users hardware