> How do you do notifications from a CRUD app on a mobile device if you can't have a native app on the device?

Facebook and Twitter are older than push notifications. SMS and email are pretty obvious replacements with little functional difference.

> Let's not kid ourselves. People rarely use the browser for something they really like on mobile if there is a native app. The experience is very different.

Sure, but you are pretty clearly moving the goalposts. Is it any more difficult to enter "news.ycombinator.com" into a mobile web browser than it is to download a mobile client?

You can use SMS or email.

There is also ongoing work to add Push API [0] support on the web as well. No Safari support though.

[0] https://developer.mozilla.org/en-US/docs/Web/API/Push_API

> How do you do notifications from a CRUD app on a mobile device if you can't have a native app on the device?

Can't service workers/PWAs handle this? While the UI may be subpar, they still have total access to it.

On Android yes, on iOS it's not supported yet.