This has not been my experience in 5e at all. I've found that healers are always welcome, but seldom necessary. (This is less true at level 1, but level 1 is exceptional in many, many ways.)
Sorry I don't buy it.
I fully expect mid- to high-level play to absolutely require in-combat healing, where a dedicated healer spends most if not all his attention (and rounds) on support spells, to keep the rest of the party standing up.
Sure, I haven't played
that much 5E (yet

) but I'm definitely seeing how monsters can take a character from 100% hp to single-digit hp in a single round, and having a healer spend a round on healing spells will then be the difference between getting that PC back out on the field and having him or her sit out the action (=acting cautiously, slowly nursing her wounds by quaffing a string of potions, trying to "buff out" with invisibility or other spells, etc)
Any combat where this is not the case, is - for me - simply a combat not dangerous and exciting enough. Sure there will be many such combats, but what defines D&D are the exciting showcase combats against hard opposition.
People like having the assurance that someone will be able to get them back in the fight if they go down, but healing your still-conscious companions is seldom the most efficient use of your action. Your time is nearly always better spent buffing or attacking rather than shoring up hit points. In many cases, casting healing spells only serves to prolong the battle.
I agree. And this makes me optimistic, if only faintly so: I still have a very hard time seeing how the party can manage as well without a Cleric or other healer.
There simply always will be a tense moment - or three - during a significant combat where a Combat Medic is desperately needed, and where the lack of a healer character will risk a PC death.
But you are still right. If the Cleric's use of Cure Wounds (etc) isn't the difference between having four heroes in the fight and only three, then yes, it is far more efficient for the Cleric to go on the offensive.
Only catch is that any such round where no fellow party member couldn't do with a substantial dose of new hit points is a luxury you won't see when things matter the most.
The best time to heal is during a short rest. Again, a healer is very useful in this capacity, so people are happy to have one. But the show does not stop without a healer. You can spend Hit Dice and get by just fine. It's debatable whether the healer allows you to have more encounters in a day because if the healer were to spend his spell slots making enemies die faster, you wouldn't need to spend as many Hit Dice during downtime (which means a non-healing class could have been just as useful).
This reasoning completely ignores between-combat-but-still-not-a-short-rest healing, but okay, let's discuss rest healing.
"People are happy to have a healer"
Not disputed. I'm trying to look at this from the perspective of the player who sees his character's spell slots drain because "we don't have time for a short rest", because "I'm out of hit dice, but we really need to move on", and "you're a cleric, we expect you to sacrifice your spells and your actions on making us look good in combat".
"You can spend Hit Dice and get by just fine."
That is simply untrue.
Yes, if the DM adjusts his adventures to match the severely reduced healing capacity of such a group. But a DM can adjust to anything, so this isn't saying much.
What you really are saying with this is: Clerics arent cost-effective.
While that would be... interesting... if true, I simply don't believe it. Wouldn't the boards be aflame with complaints "my Cleric does nothing, my group wants me to reroll a Rogue!!" if that were true.
Besides, just a cursory glance on the abilities of a Life Cleric should put that particular notion to rest.
I am happy healers can't simply out-heal the monsters' capacity to hurt you, but a Cleric can still be required, since it gives the group the important ability to focus energies on healing, to sacrifice offense for defense in order to ensure all heroes keep standing. Without the heroes standing up, there cannot be any offensive.
Another way to signal that you don't want to be a healbot is to not prepare healing spells. Of course, before the campaign even begins, you might want to mention you are doing this. Or you could be a bard and not even learn any healing spells -- that way, you still have Song of Rest to help with recovery, but no one can expect you to use your spell slots on it.
If only....
Yes, this is correct.
This is also utterly neglecting the strong pressure a desperate group will exert on the Cleric's player - not back at the inn where they all agree to let that character "do her thing" - but down in the Orc warrens, where one or several characters lives depend on the Cleric dishing out some of that sweet sweet healing after all.
And yes, you could be that Bard.
But then the problem of having a healer remains unsolved.
Congrats on creating a character and shifting the healing workload onto somebody else.
The fact you rolled up a Bard is in this way no victory - you could just as easily have made a Rogue.
Yes, the game allows for four Barbarians to strike out on glorious adventure. But how is that a commentary on the game's implicit requirement on healing...?
So, in summary, please don't get caught on the premise of my post.
I am far more interested in hearing what your suggestions are to make my wish come true, than defending my right to have that wish.