I think the real reason that you see apps on mobile devices is that an app puts an easy to use branded icon on the "desktop" instead of requiring the user to open a browser and navigate to the site. I don't think it has anything to do with lack of access to capabilities (e.g. Mint doesn't need access to my camera).
Try this thought experiment: What do you think would be the reaction from users and developers if Apple simply renamed Safari's "Add link to home screen" option to "Install App"?
I never said anything about "lack of access to capabilities". Native applications, in the vast majority of cases, are just better in every way than the similar web versions. They're faster, cleaner, and more capable. If both are being offered, it makes no sense to choose the web version.
My company makes an iOS-compatible web application with no plans for a native client right now. We use some JavaScript[1] to remind users to add us to their homescreen. But if we had the resources, we would build a native client -- it's a no brainer.
Try this thought experiment: What do you think would be the reaction from users and developers if Apple simply renamed Safari's "Add link to home screen" option to "Install App"?