Incognito mode but with a password-protected permanent session

Incognito mode was a huge leap forward in browsing concepts because, lets face it, we all have secrets. But I've noticed that I have tended to never get involved in communities that I personally believe in but don't want in my browsing history. It all boils down to the inconvenience of logging in manually each time I want to use the site in incognito mode.

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.