Moving damage off of Fizz's E is an interesting idea, it might help, but it could also push the ability farther into the realm of utility and away from damage, which might encourage tank-fizz builds even more.
It might be more balanced if the damage got moved someplace else, or made to be conditional. Maybe his E could deal reduced damage, but be capable of using the W second hit. I don't know if that's the right direction to take it, but it's my two cents.
I take issue with how you prefaced your idea:
{quoted}
So as we all know...
Saying this does not make what follows suddenly a true statement. It is very presumptuous to claim that everybody agrees with it.
People will listen better if you admit that it is your opinion instead of presuming it is proven or that it is their opinion too. Don't preface an argument with a false claim, it is off-putting.