It's quite basic and most browsers have the necessary features readily in place.
I miss a way to tell the browser that a given web-page is a web-application.
Why has not anyone implemented a cross-platform "web-app" specific HTML header tag that gives the user an option to appify a web-page i.e. for example start a chromeless browser?
It's simple. A tag in the header, and a event to trigger the browsers "install app" procedure, that basically just created a bookmark link with a custom icon, that would trigger the page in a chromeless/customized browser.
No more downloading and installing applications. Just local cache of a web-page and its scripts, that was automatically fetched on load if the user was online.
The web-developer could specify options in for example a manifest.json, like what to cache locally, what size the window should run in, in fullscreen, and if it should run completely chromeless or within a frame etc.
Most browsers have everything in place. Is there any reason as to why this is not standardized, I guess I'm not the first developer to think of this approach.
Chrome has a somewhat similar feature on desktop, but there is so little missing to provide a full fledged cross-platform browser-agnostic web-application platform. It is a future proof and backward-compatible approach as far as I know.
Standardization takes time.
There is a W3C Working Group dedicated to Web Apps. Here is a list of their publications: http://www.w3.org/2008/webapps/wiki/PubStatus.
Take for example an editor draft (ED) on manifest files: Manifest for Web apps. You'll also see they are hard at work on a Fullscreen API, a File API, and a Quota API. All very close to what you are asking for.
For example, here is the abstract from the Quota Management API Editor Draft (just a month old, emphasis mine):