Due to the offline cache, the browser gets to work downloading the entire game right away. If this was disabled, offline support would stop working (which I think is a pretty significant feature, especially for webapp-based platforms like iOS and Android's 'Add to home screen', Firefox OS, the Chrome Web Store, Amazon web apps, etc). So there's no point directing the browser to only download assets half-way through the game - it's already working on that.
Perhaps the loader layout system could be extended though. If the assets were downloaded in sequential order for each layout, then rather than having just one loader layout, you could go to any layout that has been loaded so far. So for example you could play up to level 3 if it's downloaded that far, but you'd have to wait before playing level 4 if it hasn't downloaded its assets yet.
Not sure how easy that would be to implement...