I missed your post. Only now I am looking 😅✍️Because without it formula for flux would not be useful. In most cases the reason that definitions look the way they look is just this - they are useful. You can define whatever you want, you can try to define a flux without E, or with E3 or with Eπ. Do what you want, but those definitions would be useless. I think you are wasting your time trying to dig in this issue too much. You should focus on where this definition of flux is used - and it's used in Gauss' theorem.