Well, I had a wounded hunter who was stranded outside the base, with both arms mangled, and who was, of course, immobilized (I guess that too needs to be changed).
He stood there for months, because no one would recover him, and when dwarves tried to initiate a “recover wounded” action, they will stop before the end to get something to eat or drink.
By the end, the poor hunter was starving some meters away from the entrance of the fortress, when all of a sudden, some guy come, grabbed him, brought him to a bed, then feed him and brought him water. I was like "huh, impressive, the other dwarves seldom bothered to bring him water, and this guy took completely care of it, guess it is in his personality". So I checked the personality traits of the rescuer, and there was nothing, except "He occasionally overindulges". So I thought "oh, maybe it's his friend or something". And I checked the relationship screen: They don't even know themselves.
I mean, doesn't it seems pretty rude? A fellow dwarf go out of his work to rescue you, carry you to the fortress, brought you food and water, and you don't even consider it a passing acquaintance? Err...
Suggestion #1: I think that rescued people should show a bit of thankfulness to their rescuers. Maybe this can be the beginning of a relationship: this can lead to nice situations when a rescuer and a rescued became best friend or fall in love with each other. With the future doctors / physicist / etc. jobs, maybe that wounded dwarves will show thankfulness for the doctor who treated them once they recover, or the family of dwarf "killed" by an incompetent surgeon will all have a grudge for the doctor.
And let's not forget that my hunter was stranded for months in the wilderness, wounded, sometimes starving or dehydrated, and his friends never visited him. Right now, only pets show loyalty to their owner when they are in that kind of desperate situation.
Suggestion #2: The friends of a wounded dwarf should visit him, even if he's still in the wilderness. When he's in a hospital bed, they could bring him the kind of food he likes or little owned trinkets as presents, also.
Suggestion #3: Dwarves should be more likely to stop their work to help their friends than to help totally unknown dwarves. Lovers and husbands / wives would even more endeavor to help their other half. Grudges, of course, should be less likely to help the dwarve they don't like.
Dwarves committed in strong relationships (Lovers, close friends..) will give water/food or rescue even if the "Health Care" job is deactivated, or if they're really risk-taker, disobey a "Everyone inside" (or the future burrow limitations) to protect their loved one, which can lead to interesting Antigone-like scenarios.
And talk about the previous dwarves that begun to help it, then aborted the job because they were a little thirsty or hungry while the wounded person was starving to death. Just imagine that: there was a car accident, the rescues are on the way, and suddenly the ambulance driver thinks "hm, it'll be nice to have a slice of pizza, I'll just stop by this Pizza Hut and eat a bit". And after that, he'll return to his hospital and act as if nothing happened.
Suggestion #4: Dwarves should concentrate on fulfilling the "Recover wounded", "Give water" or "Give food" jobs. They should tolerate (to an extent determined by their personality) their own hunger, thirst or drowsiness. And by the way, they should fear less the wild animals and take more risk, because now it's just ridiculous "OMG IT'S A MARMOT GET IN THE WAGON". The amount of risk taken would be determined by the personality of the rescuer, and by the relation that bound them together: A dwarf will not rush past a goblin squad to help a stranger, but he probably will to save his girlfriend.
Suggestion #5: Even if they have to interrupt their job, they'll resume it as soon as they have finished to eat, drink or sleep, unless another dwarf could take care of it in the meantime. Actually, it could be pretty nice that they wait before another dwarf is available before going to eat/drink/sleep, because theses actions last quite a moment.
Suggestion #6: Aborting a health care mission could damage the relationship between the wounded and helper. Friend which does not visit their wounded pals will also risk the weakening of their bounds with the patient, except if they have a good reason to do so (military service, jail etc.).
Finally, something I thought off when reading discussion about doctors :
Suggestion #7 : Surgeon / Physicist should be unable to operate on their family member (and maybe close friends as well), OR some of they will want to be the only one to heal their friends or offspring, discharging other medics from this task.
I think that there is a lot of space to make the Health Care more human, after all we're talking about the life of a dwarf, they should at the very least consider their savior differently afterward.