LOTS OF PEOPLE will be pleased with Ronald Reagan's choice of Utah education commissioner Terrel Bell to be secretary of education. Sen. Orrin Hatch, the new chairman of the Senate Labor and Human Resources Committee, which oversees education programs, was Mr. Bell's chief supporter. The education establishment remembers the secretary-designate for his sympathy to its concerns during his time a commissioner of education under Gerald Ford. And Mr. Reagan's close adviers are apparently satisfied that Mr. Bell will support the Reagan campaign's promised plan to dismantle the new education department and reduce federal involvement in education.

Having ourselves roundly (and vainly) condemned and inveighed against the Carter administration's insistence on creating a separate department of education, we cannot say we would be too displeased to see it put of business. But everyone concedes that there are still some important ways in which the federal government is necessarily involved in education, and with or without a full-blown Cabinet department, Mr. Bell will be obliged to think about these.

First, he needs to address the questions that the advocates of his department's creation never did answer satisfactorily: what should be the role of the federal government in the education business? Presumably, the federal mission has something to do with compensating for the inability or unwillingness of local education agencies to deal with special education needs and to ensure more equal access to higher education. But there is nothing in the current morass of rules and regulations governing the 150 or so federal education programs that gives either a clear idea of priority and purpose or a warm feeling that federal money is being spent efficiently in important public interests.

No matter how the larger questions are resolved, Mr. Bell will also necessarily be doing some managerial tasks. Chief among these are the consolidation of many special-purpose programs, and the cleaning up of conflicting regulations. This kind of management job won't seem very exciting to many educators. But it would be a most welcome change to the people who actually run the schools and who find themselves increasingly caught between the demands of those who ask that the school compensate for a variety of societal ills and those who simply want Class A service to the average child but with less of a drain on local taxes.

There are larger issues of public policy here. Many middle- and lower-middle-class families in big cities feel cheated. They pay high taxes to supprt public schools that are a disaster. Tax credits, the most widely touted solution to their problem, are, in our view, expensive and, even so, wouldn't do these people much good, since the few hundred dollars a general tax credit could provide wouldn't buy a place in anything but a heavily subsidized parish school -- and even their prices will have to go up if more children apply. Bigger vouchers that allow residents to shop among competing schools could help. But since these would replace direct state and local aid to schools -- the source of 90 percent of their money -- and since no one wants a federal takeover of local schools, an initiative of this sort would have to come from people in the localities themselves.

A heavy-handed approach not only could waste billions of dollars, but also could undermine the free school system that has provided more social mobility and a higher general level of education than exists in any other country in the world. But the genuine and legitimate distress of many parents cannot be ignored either. This is dilemma that should engage the energies of any leader of federal educational establishment -- whether he is a Cabinet secretary or not.