Elements System is kind of dumb, in my opinion. Ideally it should be scrapped and made anew, not sure how though.
But right now it could be revamped somehow.
What the game accomplishes by having a permanent element set to a weapon until the "No Element" is used is basically make everyone walk around with 5 of the same weapon, each with an element. The double damage is often good enough to shine through refinement level anyway.
So I have a bandaid fix: make elements overridable. Make it possible to just put an element on top the other, substituting the old one. Would still need to assign 5 bag slots for the elements, but would make life a lot easier and the game more enjoyable.