Pardon my cynicism, but it's hardly in Google's self-interest to have a true "incognito mode" in any browser that you use.

It's why the word Incognito in Chrome for iOS has an asterisk next to it:

"On Chrome for iOS, due to platform limitation regular and incognito* tabs share HTML5 local storage, which is typically used by sites to store files on your device (client-side caching) or to provide offline functionality. This means the same sites can always access their data in this storage in both regular and incognito* tabs. Incognito* tabs will still keep browsing history and cookies separate from regular tabs, which are cleared once those tabs are closed."

https://support.google.com/chrome/answer/95464?hl=en

Sounds to me like we need an option like delete cookies for local storage as well.