THE TROUBLE with the Legal Services Corporation is not, as the Reagan administration seems to believe, with what it does or who pays it bills. During the seven years of its existence, this organization has helped thousands for poor people assert their legal rights. But the help it has provided doesn't get to the real problem: the exorbitant cost of justice and legal services in a country that stakes so much on the idea that people must, and will, obey the law.

The system of justice now works like this. The rich -- we use that term somewhat loosely -- and the corporations are well served; they hire the very best lawyers and pay them fees that often can only be described as mind-boggling; their legal rights are fully and, usually, brilliantly protected. The poor, through the aid this corporation and other publicly funded groups provide, are reasonably well-served; they have at their command a corps of earger lawyers, most of them young, who want to make the country a fairer place in which to live. The citizens who fall in between -- the low- and moderate-income people -- are served hardly at all; they cannot afford the best, they do not qualify for aid, and they generally make do with little or lowquality legal assistance.

The administration's proposal to wipe out federal funding for the Legal Services Corporation would only make this situation worse. It would strip from the poor the key incentive most people have to obey the law and follow the rules: the belief that if you are right and the other person is wrong, the law and the lawyers will see that justice is done.

Maybe this corporation could be folded out of existence as part of a total reform of the way legal services are delivered. Maybe the money for its activities should be provided in a different way. But it would be reckless for the federal government to walk so abruptly from this project. The poor, having had a taste of what the law can accomplish in their behalf, are not likely to -- and should not -- accept quietly a return to the old days when their rights counted for nothing.

The ultimate irony in this proposal is that it would cut off legal services to the poor while countinuing to subsidize legal services to corporations and many rich people. Legal fees are often business, expenses, which are, naturally, tax deductible. Perhaps this administration, with its love for user charges, can think of a device that would channel some of that money or a part of the hefty, six-figure incomes the big-time lawyers take home into providing legal services for the rest of the community. The law -- and the lawyers -- will not be fulfilling the ultimate promise of this country until everyone has an equal chance at justice.