Browsers Accessing the Local Disk

After writing Why isn’t browser based programming or browser based IDEs more popular? – Smart Disorganized I want to emphasize and ask again.
Why aren’t the browser makers offering us a way for web-apps to read and write from the local disk?
I know that it’s a mega security issue. But it should be possible to wrap it up. So that only web-apps opened in a special mode. Which ask three times and need you to sign in blood etc. etc. (Or better, add the public key of the web-app to your browser) get to write to the local disk.
But if just one browser maker made that happen, it would be the biggest revolution in application software development since the invention of the mobile app.
Suddenly all web-delivered applications would compete on a level playing field with locally installed apps. Browsers would be more important than ever. Surely there is a huge incentive for browser makers to do this.