The only benefits I can see of "Apps", are the developer get's access to private information they really don't need.
Yeah, they get to be on the "App Store". But the "App Store" is a totally unnecessary concept introduced by Apple/Google so they could scrape a huge percentage in sales.
Web browsers have good (not perfect) sandboxing, costs no fees to "submit" and are accessible to everyone on every phone.
Apps are faster, are more predictable (no auto-reloading or rendering issues) and generally perform better IMO.
On the other hand, in reality, you're correct. I think the NYTimes app will collect more data from me than the NYTimes website.