Are there any browsers or browser addons that support something like incognito browsing but instead of the sessions being trashed after the window is closed, the session is maintained permanently but is encrypted and invisible to anyone without the password? That way, I'd just have to login once upon opening the incognito window but all of my cookies, history, and local storage would be available just like a normal browser.
With permanent cookies there might be more opportunities for your browsing habit data "leaking" via 3rd party cookies and such. But really, I always saw incognito mode as basically a way to prevent other non-experts from accidentally stumbling on your browsing later. Even with incognito mode, for serious privacy you'd need to VPN anyways.
If I were making such a feature, I'd call it "Alter ego browsing". It might be possible with a chrome extension that has the permissions to execute in incognito, to read/inject cookies, and to read/write to the filesystem.