INTEREST RATES remain very high, as President Reagan observed the other day when he tried to nudge the banks to bring them down. But the extraordinary changes in American banking help explain why they stay high. The banking system is being deregulated, rapidly and radically. As long as local banks offer 11 percent a year for five- year deposits, prospects are poor for auto loans at anything less than 13 percent--regardless of the falling inflation rate, and regardless of presidential exhortation.

Banks used to enjoy comfortable cushions of checking deposits paying no interest, and savings accounts paying very little. That was the secret of their ability to lend at less than the money market rates. Then the inflation of the 1970s created the money market funds, and they in turn forced the regulators to take the interest limits off the banks and the S&Ls. Now that the banks must pay competitive rates to enlist deposits, they are charging their borrowers those rates plus a spread that has been fattened to cover the bad loans generated by the recession.

Henry Kaufman of Salomon Brothers, the investment banking firm, suggested in a speech here last week that deregulation has gone too far. He argues --and he is correct--that the banks' job is to gather money on the highly volatile financial markets and make it available on stable and predictable terms to those parts of the economy that employ people and produce goods. Instead, the banks are getting very agile at passing the volatility and risk along to their customers.

Limits clearly can't be reimposed on the interest that banks pay. Mr. Kaufman has in mind other possibilities, like varying their capital ratios or reserve requirements. Mr. Reagan might want to tell his Treasury Department to look into it. Treasury has been giving the turmoil in the banking system much less attention than it deserves.

But, at best, public policy can hope only to improve the stability of the interest rates and to reduce them only slightly. Economic growth in the late 1970s was financed to a dismaying degree involuntarily by savers and investors caught between low interest rates and high inflation. They aren't likely to let that happen again. That's why the interest rates are going to stay high in comparison with all American experience since World War II. Americans are now having to learn to make their economy grow without the enormous flows of cheap credit to which they had become accustomed. It's possible, but it will make the recovery from this recession very different from all the others of the past four decades.