So it is boring.
That is all. When sustained healing surpassing incoming damage, a lot of drama is removed from combat.
They're burning all their actions and resources on not dying?
It doesn't have to be
all. We get this neat situation where if damage is below sustained healing, the damage is effectively zero - it just reduces the damage the healers do back.
When damage passes sustained healing, non-linearly the healing as a defence mechanism fails (often catastrophically).
And if healing is cheap enough, you get these fights that transition from snooze fests of no danger rapidly to TPKs as the damage output of the monsters changes by a small percentage.
That isn't going to win a fight, that is just losing slower. In order to win a fight, you need to spend those actions and resources on actually winning. (Achieving objectives, defeating opponents etc.)
That is the beauty of the temp HP idea: since temp HP doesn't stack, there is an inherent encouragement to do things other than heal. If they are taking so much damage that other party members are using their actions and burning resources just to stop them going down, then either they are either getting focused by all the opponents, took a chain of crits, or are holding the line against a superior foe - in which case it is just good party play to try to stop them from dying.
You seem to be confusing "good tactics" with "good game design". A party faced with a certain situation with certain resources doing X might be good party play, but good game design decides what kind of situations a party faces and what kind of resources they have to deal with it.
"We negate the damage threat" is great tactics, but poor drama. Because now, any damage threat below a certain threshold has no dramatic impact -- there is no risk.
If negating the damage threat is
hard or
impossible, now drama from damage is more continuous. Ie, with cheap fast healing of 20 HP/turn, "I took 20 damage out of my 60 HP" is a trivial problem you can deal with forever (while slots last), while "I took 40 damage" is an emergency and the PC is dead next turn regardless of what the healer does.
By level 6, level 1 slots might be "cheap", so in baseline 5e cheap healing is about 6.5 HP/round at level 5 (healing word, +4 wisdom). A life cleric dip using 2nd level healing spirit and healing word heals 15 HP/round (and has actions free beyond the first). That is a good 30% of a fighter's full HP bar at this level - already we are getting into the space where foes that don't threaten to drop a PC in a single set of attacks aren't a serious threat against PC healing.
And as I have stated, Life clerics are (in my experience) already past the point of "healing that is too good".
I think that this is what you and many others of the "Kick the player when they're down" opinion are not getting: We do not like that optimal healing is performed at 0HP. We think that the mechanics rewarding that playstyle encourage degenerate gameplay. We would like the mechanics to encourage using healing while the character is still up. We would like character concept of someone who can support the party by healing to be a viable option.
Again, optimal healing is not performed at 0 HP. A PC that is dropped to 0 HP is likely to die before any healing occurs. Only if the PCs get lucky, or the DM pulls punches, does the 0 HP PC survive to get healed.
In the extraordinary case where a PC at 0 HP gets healed before they are dead, they are likely to be one swing away from being back at 0 HP and (again) almost certainly dead before a heal can land. So they can sacrifice themselves to get in a few more swings, or disengage and run for it while hoping someone else in the party slows the enemies down.
A PC at 0 HP is a dead PC - any surviving PCs who hit 0 HP are those that won a hail mary chance of survival.
Punishing the player for their character dropping down, whether through hitting their character whilst they are bleeding out, or death-spiral-inducing conditions inflicted on players who do drop to 0HP isn't a useful attitude unless you give the players more options to prevent their characters dropping to 0HP in the first place. Healing is one of those options.
The PC hit 0 HP, they already lost.
You avoid hitting 0 HP by doing stuff like "not fighting", killing foes before they kill you, healing up before continuing the adventure, etc. Short rests are great for this.
A level 6 fighter with 16 constitution has 58 HP, a second wind (per short rest) of 11.5, and HD healing 51 HP. In a single fight the fighter takes 69.5 damage to drop (nice). If they take 2 short rests, they get to take up to 58 + 51 + 11.5*3 = 143.5 damage before they drop.
The level 6 cleric who heals with cure wounds has 12 spells over a day with total levels of 21 for 142.5 HP healed. With 14 con, they also have 45 HP and 39 healing from HD, contributing 226.5 HP/day. This is already bigger than the Fighter's contribution by half-again.
Upping this to a Life cleric 1/Druid 5 who uses L 2 healing spirit 4 times, mass healing word L 3 3 times on 3 targets, and L 1 cure wounds 4 times we are talking 353.5 HP healed/day, almost 2.5x the fighter's contribution.
As I have stated, as I have observed, healing in 5e is at the edge of being too fast, and life clerics already push it over the limit. Further boosting just makes the HP of non-healers more irrelevant, and the current HP of a character just a measure of "do you die in one round? If not, not a danger".
I've seen it in 5e, 4e, 3e, OD&D, and piles of other RPGs.
Make players fear hitting 0 HP, and the yo-yo healing problem goes away. If foes that drop a PC to 0 HP are near-TPK situations, then the damage flux of monsters that DMs design encounters around is going to be
lower, because you don't have to drop a PC to 0 in 1 round in order to drive drama with damage. So you get lower damage monsters
for the same amount of percieved threat.
And suddenly, the heals that already exist are more substantial. If you have 60 HP and are taking 15-25 damage per round, a 10 point heal (or even a 6 point one!) doesn't stop you from dropping, but it sure slows it down.
On the other hand, if a threatening monster does 40-60 damage per round, then that 6 or 10 point heal looks a lot more pointless, and saving it for the PC dropping to 0 HP makes a lot more sense.
And there are a pile of ways to protect a PC that aren't "outheal monster damage": I mean, try dropping a sanctuary if you go after the ally and before the monster - suddenly they need to make a wisdom save to continue to focus fire on the wounded PC. The PC can ignore the sanctuary and attack, it is only a 1st level spell slot and a bonus action spent.
...
But anyhow, that is your game and your problem. Just keep an eye out for the effects of easy healing causing monster damage to have to inflate, and the resulting non-linear mess you run into. Also, keep an eye out for an extra cleric adding more durability to the team than another meatshield. Also, keep an eye out for slow combat.