ALBANY, Feb. 8 — Pity the New York State lawmaker, if only for a moment. For years, the state’s senators and Assembly members have been widely tarred as barely competent time-servers, hostage to their all-powerful leadership and resistant to change. Two years ago, a study deemed New York’s the most dysfunctional state legislature in the entire country. Last month, a panel that was asked to pick finalists for the vacant state comptroller’s office passed over several Assembly members angling for the job, suggesting they were unqualified. For a crowd where aspirations to higher office are common, it was the last...