The subject kept coming up all the time. “Everybody I talked to over the past year has been saying, ‘Ugh, it’s so awful,’ ” former Mayor Edward I. Koch said recently. At lunches and dinners, in meetings with clients, law partners, fellow alumni of public service, business associations and good government groups, the conversation invariably turned to the political chaos in Albany. “I finally said to myself, somebody’s got to do something,” Mr. Koch recalled. “And if no one else does anything, notwithstanding the fact I’m 85 years old, I’m going to throw myself into it.” So Mr. Koch is...