Not only promotion, even demotion.
For LBing 5*s, I personally think it depends on which you want to do better in, PvP or PvE.
For example, in the current event, CC cards like petrification seem to have a much lower rate of success. This also seems to be true for event bosses in Moon quests. Straight up high damage cards like Shimako's 840% one would shine pretty well in these high HP boss events, I think.
On the other hand, CC cards like petrification and instadeath do very well in PvP Duels.
The safest route is obviously Healers, as they are useful for both situations.