It would be nice if the "doctor" type skills suggested were just part of the Health Care job that exists currently, rather than something new. Health Care seems atm to be little more than glorified hauling - taking wounded dwarves to their beds and then hauling them food/water just before they die of starvation, unless the Carer gets distracted by a shiny object or sock.
MAybe have a bone-mender workshop which works something like butchers and tanning workshops seem to for their basic tasks? So you don't have to manually queue "Look After Bleedy McSquished" jobs but they queue up themselves at the bonemender workshops whenever the game deems the bedridden need looking after, and relevant Health Care enabled Dwarves will go sort out the patients when they can be bothered.
The Health Care skill could be proper skill then, with higher ranks giving a hgher chance of healing nasty wounds.
Not sure it would be a great improvement, thinking about it, but I know I would be more reassured that they will do something if I can build a workshop and see the jobs queuing and being done, rather than hoping the random onlookers bursting into my Mayor's bedroom are going to do somehting useful like mop up the blood and tell him everythings going to be fine, rather than steal his socks.