Just looking at the advanced stats and realized that outside of Draugrkin, there are almost no sets that apply flat damage to skills.
I know this would be risky with Magic Damage due to Arcanist laser, but I think it would be fine for other damage types as they generally tick once per second at most.
Eg
5 Piece Bonus
Your Frost damage over time effects and Chilled status deal an additional 500 damage, but your health recovery is decreased by 200.
Your Flame damage effects deal an additional 400 damage to Burning targets, but you direct damage abilities deal 12% less damage.
Your Concussed status effect deals an additional 1000 Shock Damage and sends out a bolt of lightning to a nearby enemy that deals 1000 Shock Damage.
That Shock one seems a bit op I know. But it was more to illustrate the idea and point that Flat damage is kind of a dead stat currently.
Another option is to add additional CP slottable stars that have the same effect.