I play support characters quite often and while I will often cast a cure wounds spell to try to prevent a character going down, in the majority of cases I would have been better off using those resources beforehand, to prevent that damage.
Preventing damage through effectively ensuring that there are less enemies hitting your party in the first place will almost always be more efficient that trying to cure it afterwards.
The problem is that a game where healing is good universally ends up with either rocket-tag, or non-threatening combat.
Rocket tag is when the only way to kill a PC is to take them out before healing can land. You can see this in a pile of games.
Non-threatening combat is when damage does nothing but drain the tank of the healer. Taking damage isn't a threat, it is just a resource drain on the healer. When the healer runs out of oomph, the day ends.
Both of these where true in 3e. Healing could outpace damage, healers had far more healing resources than warrior types had HP, and a real threat either wiped a target's HP out in one blow or bypassed HP entirely.
4e moved a huge amount of a healer's power budget to the target PC. Running out of HP was a single-encounter thing mostly, and the daily resource drain was on daily powers and healing surges.
5e, at least initially, moved to a model where running out of HP and HD is a daily resource drain. A melee type can contribute more HP than a healer can over an adventuring day, and the use of healing was more of an emergency thing than anything. Spell slots where better used in ways besides healing.
What I see in this thread is people seeming to ask for 3e style healing, what I consider the most boring era of D&D heal-wise; healing that makes non-fatal damage trivial.
The problem I have is that it isn't a huge gap between "healing isn't worth doing in combat" to "healing makes damage trivial". The life cleric in 5e almost bridges that gap.
Moving to 4e style healing would be one way; in that model, you'd allow magical healing to burn hit dice and heal extra that way. Each use of healing would have more impact, pushing it over the "not worth doing" to "big enough to nullify incoming damage of a threatening foe". This does push the game further towards a 5MWD, as more resource can be expended in a single combat (HD), leaving fewer for the rest of the day.