Especially with single-page applications, I would love for there to be a way for a page to have either access to persistent store or network connections, but not both. A site could load all resources, then announce to the browser that it would like to have access to whatever it stored the previous time. The browser would grant access to the local information, and simultaneously take away access from ever initiating a network connection again. A newly loaded copy of the page would start in the same state, able to pull in new resources, but unable to read or write local information until it again gives up the right to exfiltrate.

It would be a one-way street that way. The page can take any network information with it into the private cave, but nothing from the cave may ever come out, nor may it even know if the cave is empty before taking that irreversible step.