Speaking as a user, I do prefer native apps that actually do the things that you have mentioned (i.e. use idiomatic UI for the platform, integrate with its features etc).
The problem is that the vast majority of the apps that we're talking about here - the ones that replace websites - are little more than a web app repackaged in the app store. So it still has all the downsides of a web app UX-wise, while also working around any privacy settings that would have applied in the browser.
The problem is that the vast majority of the apps that we're talking about here - the ones that replace websites - are little more than a web app repackaged in the app store. So it still has all the downsides of a web app UX-wise, while also working around any privacy settings that would have applied in the browser.