there are only 3 ways for a doctor to see any work in the game:
hostile creature injures a dwarf
pet spazzes and injures a dwarf
and (lets face it) player incompetence.
a good or tedious player will never see a doctor used and even a !!fun!! loving player will see very little use for a hospital and medical staff. it's almost easier to leave your dorfs to their misery when they get injured and a fort can easily survive with no medical care.
i propose a simple solution to this. accidents, not noble accidents but genuine everyday accidents.
Urist McClumsy has fallen down the stairs
Urist McMason has chissled his own hand
Urist McDrunk climbed a statue and fell off
Urist McSmelter has received burns
so why not? dorfs are proven to already lack basic survival skills. having a chance for dorfs to wind up in hospital would make it much more necessary and give more skill to doctors for wounded milta, ect really needed attention. other ideas to expand on non combat/serious mining accident related visits would be illnesses and child birth. illnesses could even come form vermin in the food stores or contaminated water.
As long as these don't happen too often, I support this. Probably 1 accident per month, per 200 dwarves would be a good starting point. At that rate, you'd be
lucky to see a single randomized accident in the first year or so of a fort.
I would also suggest biasing the selection of injuries based on expected treatment requirements (both type of skill required and the skill level). Injuries that just need to be cleaned and bandaged (and maybe with one or two stitches) should be more common than those that require the attention of a surgeon or bone-setter.
And injuries should be archetypes, so the "climbs on statue and fell off" would be "<dwarf> climbed on <built-furniture> and fell off, causing <fall-injuries>". Similarly, for the workshop things, "<dwarf> was careless at work and <task-related-injury> [at <workshop>] while <task>", which would, of course, have a chance of firing while the dwarf was performing a task. Optional workshop so fishing and hauling can use it.
As for falling down stairs, I think that one should be avoided, because last time one of my dwarves fell down a stairs, it was 20 levels and only giblets were entombed.