The main attraction for 64-bit ARM is, apart from the obvious future proofing, it has a redesigned and much more efficient ISA. It also has the optional secure enclave feature which Apple used for TouchID and now FaceID. That feature doesn't actually require 64-bit per se, but it is only a feature of the 64-bit ARM architecture. As an aside, is anyone else using it for anything? I'm only aware of Apple using it, but technically it's not an Apple exclusive feature.

Your 'focused on power saving' point is correct as far as it goes, that was their intent, but unfortunately the power saving benefits of BIGLittle turned out to be much more modest and full of caveats than hoped. It turns out that a fast efficient single core that can complete an instruction in less time, then quickly shut down into a power saving mode, is more efficient in power terms for most cases than a slower lower powered core taking longer. As a result Apple's fewer faster cores approach turned out to actually offer better power efficiency as well. Since then Apple has also adopted BIGLittle, it's not a failed technology, it's just that the inflection point when it becomes worth doing was at a very different point than previously realised. Whether thats down to luck or judgement on Apple's part is moot.