Does “the best machine for AI use” apply here considering these models are still server-side?

The play here seems pretty evidence, if I may assume. Apple creates an interface that is generalized enough so you can easily swap models, and while Claude is preferred by Apple today, it may be any provider or even local models in the future, and the APIs the developers use remain the same, so "migration" becomes easier.

for the on-device model, yes it runs on the Neural Engine (at the moment) so a newer chip means faster, cheaper local inference. For the server side path this Claude package is about your machine is irrelevant since it's a network call. The same API covers both, so "best machine for AI" only bites when the session is actually local.

But we can imagine that the balance of what's on-device vs what's remote will move continuously towards the former as time, improved HW and improved local models keep progressing

I would think so, as “use” doesn’t specify implementation. If you use a word processor it may be running locally or remotely.

From a user’s perspective, it doesn’t matter.

Apple's been trying to make the marketing appeal that "Private Compute Cloud" is also a hardware project. Given it seems to rely on low level details of device Hardware Security Modules, it's maybe even at least a little bit more than just "marketing spin".