This will bring you back up from unconscious, with a few hit points. Effectively 35 of those 40 incoming damage points are simply gone. And the best part is - the next time the monster hits you, 35 of those 40 damage points are negated once again.
Each time you the Cleric
1) save movement
2) save spell slots
3) save time (since you only spend your bonus action, you can use your regular action for offense, to help defeat the monsters)
A good articulation of the extreme case.
Of course, there are cases that'll be less extreme, where many enemies, or enemies with multi-attack, are chipping away at you with little bits of damage, so waste less when they drop you, and instead move on and drop someone else with their remaining attacks.
To talk around to my point, the major issue does not seem to be the heal-from-zero then.
This stems from the desire to have the most efficient use of action possible, no matter what.
From 'smart play,' yeah, FWIW. The caster has a number of reasons to not heal allies & to heal them with the lowest-level slot practical, and heal-from-0 just adds another big one, 'efficiency.' When it's already in the caster's interest to hold off on healing so he can take another action, or heal with a lower-level slot so he can reserve the higher level slot for more personal-glory uses, being able to analyze the options and determine that the self-interested choice is also the 'more efficient' (and thus better for everyone but the guy getting dropped each round) one, well, it becomes a cinch.
Now then, looking back at the OP's proposed solution. What is the most efficient use of the Healer's action if they want to still be combat capable and do the least amount of healing necessary?
They don't heal.
Prettymuch, it 'balances' the efficiency of heal-from-0 by punishing it, rather than just removing the efficiency. The same is true of imposing exhaustion.
OTOH, counting negative hps can also lead to problems. If you only go to -10, for instance, and then die, high-level games will see almost as much instant death as 1st level ones, because damage scales pretty dramatically in 5e. If you go to high negatives, like -max, then when someone gets deeply beaten down, not healing them at all, again, becomes the best option (let them wake up and spend HD later).
Another option, though a complex one, would be to count negatives up to some limit, but not have PCs simply die at that limit. So you track to -10 or -(10+level) or whatever makes sense given the psychology of the healers at your table, but still only die if hit for -max. Waiting for allies to drop is no longer hands-down most-efficient (and thus no longer as good an excuse to use your slots & actions for yourself).
Another thought: a minimum slot cost to healing a dropped ally. Any cure or heal spell can work on a conscious ally, but if he's at 0, it must be at least a 2nd level slot, plus another for each failed save. That'd make it more in the casters' interest to heal before allies drop, I suppose.
Another 'nother thought: Change healing word to let the target spend HD, in addition to the hps restored by the spell - /if he's already conscious/. That'd make it more efficient from the caster's point of view, and more effective from the target's. Could be combined with some of the other ideas.
Edit: Sorry, another, other, 'nother thought: It's probably clear from the above, but part of the problem is also that casters use slots to heal, and slots have lots of other very powerful, useful to the party, and spotlight-grabbing spells they could be used for. If you had more HD, and ways to use them in combat, to the point that the party could more or less depend on them, you'd eliminate much of the need for devoting slots to healing in the first place, and heal from 0 would be less important (it'd still have anyone able to trigger HD for another 'playing chicken' in the name of efficiency, but it wouldn't be as pernicious). Of course, the casters with healing on their list would 'need' fewer slots, since the game clearly must assume some routinely get devoted to healing...
