there are many mundane reasons to use incognito mode. and the system would work in a way that the user will not even know the decryption key since it can be generated on the fly for each session.

the browser could even encrypt all their data by default. (but for non-incognito mode with a known key) it could then write the normal and incognito data in such a way that you can't even see that there is incognito data in there if you don't have the incognito key