But, was initially confusing because I couldn't find their app in the app store, where I was expecting it.

In my experience this is a huge problem. Along with the process of adding to home screen - people just don't get it. Once they have it installed they're very happy, but getting them to that point is difficult.

1. You can have an icon for web apps

2. That's only true if the web version is crappy and overloaded with ads and trackers. A decently designed

I prefer mobile web for publications, because it's just a link that doesn't impact my phone. The native integration usually only brings annoyances, like unwanted notifications or sucking the battery to fetch articles I may not read.

Apps are for applications. For content, nothing beats the web.

Exactly. I don't want to read your article over your own dedicated app, I already have a perfectly good browser...

...BUT! I also hate applications made as webpages, because no one can perfectly hide the fact it's not native. In webapps, UI pretty much always lags somewhere, breaks down completely under spotty Internet connection, or does something weird because there's no way for webapp to replicate every aspect of expected UI functionality of user's phone.

3. It should working without a network connection, unless there's an over-riding need

Edit: btw, she's a school/music/languages teacher, so she has very little technical background. In her own words, she "touch[es] everything until it works".

That was there, certainly, but what I read most was the resource cost of covering many platforms, something I completely empathise with.