You can't possibly believe that. Do you have an application on your computer for every website? Why not? Don't your arguments hold up there as well? Web apps designed for mobile can be just as good as native in almost every situation, sometimes better. My vision isn't so hot so I like to zoom and stuff. Some web apps don't let you do that, but I don't know of any mobile apps that allow that.
With the ability to use local storage and manifests for storing web content locally like it's an "app" that updates itself when it opens if it can. You can access everything even when you aren't connected to the network if that's your use case in this situation. Web apps can open the camera and interact with it, you can use GPS, you can do pretty much everything except looking at your phone's data which I don't want them doing anyway and they could get similar information from Facebook or Google if I wanted them to do so.
You want it to look native? Device recognition will work for that. The myth that native always is better isn't true. Can it be better? Sure. Will it be? Probably not because it takes more effort as a developer, new versions of the app have a longer deployment time because of the application store, and the audience will be smaller as well so there is less incentive for a company to pour resources in to the app. Plus you have to develop 2 different versions of the app or ignore half the possible users.
In summary, the slight edge native has on capabilities lives in a small space that most "apps" (native or web) won't use, and making the thing work as well natively as it does in the browser is harder, so most developers or teams won't get that far let alone going beyond the web experience. Finally, maintenance and agility are a pain in the ass so a native user will always have to wait longer for there usually inferior experience.