My view is this: Healers focus on keeping the party alive, with extra duties like mitigating damage, debuffing enemies to deal less damage, buffing allies to deal more damage/beneficial effects as the game's system allows. However, that's all part of the overall 'duty' of the healer. And that 'overall duty' is the same as the other two roles of the trinity: do what is necessary to aid the team to successful completion of the content. And yes, that means that if there is a dead GCD where you do not need to heal, there are no buffs or debuffs to refresh, nothing else that takes priority, it means 'do damage, even if it is really weak', because every little helps and there's times where the boss enrages at 0.1%. As a personal anecdote, my first clear of P8S was so close, the enrage had finished it's cast and people were dying in that staggered fashion. And my last action was a swiftcasted Glare. Had I not done that, it's entirely possible that we'd have actually wiped.

Dealing damage is part and parcel of being not just a healer, but a team player in a team game. We don't tell the tanks to 'only keep aggro, damage is the DPS's job', we don't tell supports to only stand in lane and leech XP from the carry, we don't run around as Lifeline in Apex Legends only pressing her Tactical to heal people. No, we also find time to do damage as tank, harass the enemy laner as the support/set up ganks, and shoot at people in Apex, even as Lifeline. We do what we have to, to raise the chance of success for the team. Even if it's not necessarily in the name of the Trinity Role we're assigned. After all, we don't complain that Melee can heal themselves with Bloodbath, do we?