Many and probably most common neurologic conditions are treatable (as mentioned above: stroke, migraine, epilepsy, Parkinson's, MS, etc). There are a handful that are reversible and even curable (i.e. brain infections, stroke in certain cases, vitamin deficiencies, Guillain-Barre syndrome, etc).
This is similar to most sub-fields of medicine that diagnose and treat chronic conditions (i.e. heart failure, renal failure, liver failure, etc.) and reversible/curable conditions (anemia, infections, etc).
Even when one cannot treat the underlying disease itself, one can still treat the patient. i.e. physical, occupational and speech therapy, supportive measures, education, community and social resources, psychosocial support, etc.
In being a physician, one has a much larger role than simply diagnosing and treating disease.