Fifth Element
Legend
We don't know, and yet in the OP we have "A 20th level fighter will have HD20 and do 20d[w] damage."It's not a false premise if we don't know how damage dice and hit points will progress to 20th level. It's just a guess.
You don't know if fighters will roll 20d or not.
We don't know for certain, but currently all signs point to no. So you're suggesting a solution to a problem that doesn't exist.