For starters, I want the design to reflect how the game is actually played. To make a long story short there will ALWAYS be significant downtime where you're DPSing unless they fundamentally redesign combat in this game from the ground up. Straight up, with the ways encounter, gearing, and stats are designed there is no way around this. So embrace it, realize that DPS is as much a part of our play as it is for tanks and make combat more interesting.
Now, beyond that I'd also say give us more ways to contribute, and ideally I'd wrap the two together. Sage is actually a step in the right direction with DPS spells providing passive healing, but ideally I'd go with something similar: Allow our DPS during downtime to contribute meaningfully to our support role. It could be something simple like DPS actions contributing to fairy gauge or lilies, or something a bit more complicated like having combos for our spells with the finisher granting a party-wide buff.
Recognize that we'll spend a fair amount of our time DPSing especially as player skill and gear rises, but wrap that into the core support mentality.