Off the top of my head, mobile Safari can't handle push notifications for new content or downloading videos to watch later. I'm sure there are other problems with it as well.
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.
I believe it's Netflix that prefers that users use the app.