Offer source so people can run it locally.
What use is a local app that is unable to access the resources it requires due to the Same Origin Policy? Some of the resources are dynamically generated by the web app's server. Even ability to download static resources locally as well would fail because Chrome considers each file in the file: scheme to be a separate origin.
If you instead refer to storing all resources on a computer owned by the user, there are two things likely to happen. The first is unwillingness to share source code: "You can use the app on the public server without charge, or you can license a copy to run on your own private server for $9,999." The second is network effects. Consider a web application that allows users of a particular server to interact, but user accounts on your private server cannot interact with users on the public servers. So good luck getting the majority of users to use your private server instead of the public ones.
If you want more concrete examples, consider whether the publisher would be wiling to offer the source code for Google Maps or H&R Block At Home or Netflix or an HTML5 multiplayer game with greater-than-hobbyist production values. Or what would be the business model for funding the continued development of such an application as free software?