ITS ROUGH being a mayor these days. Tom Moody, the mayor of Columbus, Ohio, and president of the National League of Cities, vented some common frustrations this week in a speech assailing citizens who expect public services "for free." Mr. Moody, speaking in California, complained about people who vote to slash taxes and then object to program cuts. And he suggested that this reflects a "new immaturity" - typified, he said, by parents who "will not accept the responsibility" for helping teach their children to read, demand expensive remedial courses in public schools, then "scold the school board for extravagance and the teachers for sloth, and delight in citizen 'revolts' that aim to gut the school budget."

Mr. Moody thinks such public petulence is growing. His view may be clouded by the school-bond battles in Ohio, which began long before Proposition 13. But if voters elsewhere are starting down that road, there is indeed cause for concern.

In the constructive part of his speech, Mr. Moody asserted that asking less of government is not necessarily the best or only remedy. Instead, he emphasized finding better ways to provide and pay for important services - by sorting out federal, state and local responsibilities, overhauling tax structures and managing programs more effectively. Mr. Moody noted that a local-option payroll tax has enabled Columbus to cut property taxes to 8 percent of the city's general revenues, thus presumably spreading tax burdens more equitably.

Now, restructuring government is hardly a new prescription, nor one that is easy to fill. The wrangles over welfare and state financing of education show how hard any major governmental revamping tends to be. Still, it's encouraging that the League of Cities and other national groups, along with many jurisdictions, are tackling these perennial problems anew. This time around, the general exasperation may turn out to be of some help in getting necessary changes made.