Being able to download/cache content reliably would be welcome, on all browsers. However, I haven't seen a good example of using PWAs' storage APIs to cache video content, Safari or otherwise.

Lack of push notifications in iOS Safari is a giant shortcoming. It's especially baffling since it exists for Safari on macOS. That being said, I can't say that Netflix's push notifications (in the app) are particularly useful (to me). They always spam me with newly released yet irrelevant in-house produced titles.