I think being constantly in pain, or suffering from lack of breath, or having trouble doing everyday things for lack of usable limbs _could_ quite realistically drive someone mad. Remember that this is a world without effective analgesics or prosthetics (and quite likely a society that's not very supportive of handicapped people). My current "major injury" dwarf got a lung permanently disabled in an accident (forgot dwarven prioritising so of course a floor tile adjacent to a bridge was built before any actual support was in place), suffers regular bouts of being "winded" and gets a constant yellow "shaken" from major injury thought. She went "stressed" after a bit over half a year and is still at that state almost a year after getting wounded. "She can handle stress", so that ought to be a slower-than-average progression. She has grand master skill at discipline by now...
I don't find it at all unrealistic, i just find it slightly frustrating that there's really nothing you can do to help such a dwarf (apart from the bay12-approved lazy sociopath ‼treatments‼).
Ironically enough, I've had the exact same problem with the exact same injury, the left lung being rendered unusable. Unfortunately I doubt it can be cured by prosthesis (suspension of disbelief can't quite cover wooden lungs) but at least with a legendary dining room and really nice bedrooms I can keep him from going insane for another year or two of service.
That seems a good suggestion for useless limbs. Crutch walker could cover their use. Incurable nerve injuries should only be those to the spinal column and brain.
I don't know about crutch walker being used, maybe a separate skill for prosthetic leg or hand use, considering that there is a distinction between brewing with "plants" of "fruit" it seems more dorfy to have separate skills for them... And I feel like dwarves with lower spine injuries should be able to carry themselves around in a wheelchair or something to bypass not being able to use their legs...