I like the idea. I think something similar is already in place: there are JS libraries (eg. jquery) which are required for a website to be rendered. If the library is loaded from a central place (eg. google.com, or the creator of the library), then it can be cached and it doesn't have to be downloaded every time. In the same way, there could be different downloadable browsers, and you could require one for your website.

As a developer, it would be amazing if I could make every user run the browser I used to develop and test my website.