IT WAS A FAMILIAR symbolic show: President Carter and his entourage touring the desolate South Bronx in October 1977 to demonstrate concern for the cities. There was no better backdrop, in that no area has a greater expanse of devastation. But there was no worse impression to leave than that such places might be revived any time soon.

What followed Mr. Carter's symbolic trip has also been predictable. New York City officials hustled up ever-more-costly South Bronx redevelopment plans; the last involved about $2 billion, mostly in federal funds. Administration officials, while making friendly mumbles, kept edging away from any large, long-term commitment. This month the whole shadow-structure of plans and promises collapsed when a city board rejected the housing project that Mayor Edward I. Koch wanted to start with.

It's just as well. Everyone, from the nation's taxpayers to the people still stuck in the South Bronx, has been spared a costly, depressing failure there. For if you add up that area's problems -- the many blocks of vacant lots and vandalized buildings; the high percentages of people on welfare and out of work; the drugs, the crime, the flight of jobs and hope -- it's hard to see how any project that can be paid for can make much of a dent. To put it another way, the urban strategy that is currently popular, shoring up existing neighborhoods, won't work where there is no real neighborhood left to save. And the old bull-doze-and-build approach to renewal produces only endless public outlays and frustration unless private employers and investors can be attracted to the scene.

Economic revival is, of course, one of this administration's main urban-policy themes. All the talk about "leveraging" boils down to a commendable desire to use public funds to attract private jobs and capital. But, understandably, few officials are eager to emphasize publicly the other side -- that it is futile to pour new subsidies into areas so ravaged that they hold out little hope for private returns. Nonetheless, economics may dictate giving up some territory, shifting some people to less unhealthy areas, plowing under some rubble and building nothing in its place -- or building parks or planting vegetables until some industry is eventually attracted to the land.

Elected officials, especially local ones, can hardly be expected to go around saying anything like that. It goes against the grain to write off any ground or admit that the immediate future for some areas, as places to live and work, is downright bleak. Humility can sound too much like hopelessness. Yet for New York, and other cities with a sector from which most life has fled, accepting that can be a kind of liberating step. It can free everyone to concentrate his energy and investment on helping needy people and bolstering sectors that still have some economic strength and social cohesiveness. And it can free everyone, too, from symbols and banners -- such as saving the South Bronx -- that only fly in the face of reality.