Agreed on this. I'd also add a couple of things - first, deeplinking is a partial solution that a ton of (even really sophisticated) products have yet to adopt (I'm looking at you LinkedIn). Second, push notifications for iOS are still a massive pain to implement. I see sophisticated dev teams struggle getting this set up all the time. Layer to that all the different ways people use emails (marketing emails, lifecycle emails, transactional emails etc) and try to turn these systems into generating push messages, at scale, and you have an even bigger challenge. Times will get tougher before they get better.

EDIT: Focused on iOS because, as of today, that's still where the money is. From what I understand setting push notifications up for Android is far more straightforward.