Implementing this is problematic because depending on the filesystem, it might not be possible to "wipe" a file by repeatedly writing over it. For instance, if it's a log structured filesystem. On the other hand, you might not even need to overwrite in some cases, eg. filesystems on SSDs with trim support. Also you don't need 35x overwrites. There's no evidence that even 1x overwrite can be recovered on contemporary hard drives.
Storing the history in memory also solves this half of this problem, and surviving a reboot is not necessary to ensure and audit privacy.
edit I'll stop. I can understand the flaws in this setup, I don't understand why you think it isn't possible/wouldn't solve the problem.
What actual evidence do you have that incognito mode is wiping the history at session end?