Instagram users only use instagram because it provides access to those functionalities.
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That's irrelevant. It doesn't matter that making a fat client for HN isn't necessary; that's completely beside the point. You're looking for reasons to ignore the stated premise of an analogy rather than accepting that the premise would be true.
It's like this. Say you were beginning to explain how network services work with an anecdote: "Say you need to go to the market to get a carton of milk." Suddenly your listener stops you and says, "But I don't like milk."
If your response to the above paragraph is, "But I don't know how network services work," then, congratulations, you can look forward to an exciting career in either comedy or politics, depending on whether or not you were serious.
It certainly isn't that the app provides functionality that isn't avaliable through the browser, but somebody decided that it was worth spending development time and nagging users over. So yes, there are things that can't be implemented through the browser and require an app, but it's incorrect to state that nobody develops an app unless they absolutely need to.
HN essentially is a service that provides only a couple of text views to list and read submittions and their discussions, and requires zero processing or interaction. That's hardly a challenging problem that requires a fat client.
If however we were discussing an application that required significant data processing, access to your personal data, or even access to photo ir video input... You'd hardly be able to implement something with HTML+CSS.
Case in point: twitter is very usable as a website but instagram is not.