I am a programmer and it would not be so difficult to have created an option for the user to choose to keep or not to keep the exif data or even to keep at least the exif data that matched on all the images in the stack.
Any photo software that preserves the exif data of the RAW file during focus bracketing? Well, the two I have tried so far: Photoshop and Helicon Focus, they keep the exif during focus bracketing