Jester David
Hero
I believe that, in 3E, in-combat healing was also a significant factor in the game - at least at a number of tables.
There seems to be some disagreement on whether, in 5e, in-combat healing is important. That suggests to me that it is, at least in part, a table thing.
I agree that inspirational healing as a post-fight thing, rather than rousing or rallying, isn't very inspiring. I personally don't like it much for clerics either - when you look at the archetypes for prophets and wandering miracle works, very few of them perform their healing as a form of post-combat medical care.
Healing was important in 3e, but it often came as much from wands as clerics, unless you were house ruling character wealth.
Still, healing was limited, and the cleric was at its strongest when not healing. So there was a strong incentive not to heal. And even in 3e - where you quickly healed more for a spell slot and had more healing slot - damage quickly outpaced healing making in-combat healing a trap.
You heal even less in 5e and monster damage is higher, so healing is even more of a trap. And combats are faster, lasting fewer rounds. You're almost always better off using your action to attack or take the offence.