Technically Apple does support offline via the older manifests mechanism (and "Add to Home Screen" which invokes it remains prominent in the safari share sheet) though it's a lousy (and pretty buggy) experience.
Interestingly they don't support any sort of web notifications on iOS despite having added local notifications ( https://www.w3.org/TR/notifications/) in macOS 10.8 and remote Safari Push Notifications (built on APNS) in macOS 10.9.