We would heal more if, after keeping everyone alive, healing ended encounters quicker.
Wiping in a fight is terrible; wastes so much time of the clock. It feels so good to save a catastrophic run because that is a possible wipe avoided.
Dead players stop contributing to the fight, and this waste time. Even when they mess up, I will heal them, as long as they are trying - since that effort generally is rewarded.
Besides that, healing can't really affect the fight. Damage spells do, but the ones we have are boring. Alas, since we want to be useful, we press them out of obligation.
The drive to keep everyone alive and the drive to do DPS come from the same source, at the end of the day. DPS is not king. The clock is.