As attorney generals go, Edwin Meese III comes high. He has submitted to us taxpayers a bill for $700,000 in legal fees he ran up while under investigation by independent counsel Jacob Stein, who was looking into charges aired during Senate hearings on Meese's fitness to become attorney general.

Having been certified as nonindictable, he is -- under the law -- entitled to seek the money. The question is whether he is wise to do so. His difficulties in the first round of hearings arose from the fact that he is a relatively unmonied man trying to keep up with the super-rich in the upper reaches of the Reagan administration. The hearings explored a pattern of half a dozen people having helped Meese financially and ending up with federal jobs.

A weakness for pricey lawyers is not reprehensible. We all want the best professional help when we are in trouble. But Meese is part of an administration that sought to limit the fees paid lawyers who bring public-interest cases against the government. The cap sought was $75 an hour, and it was seen as an effort to discourage those advocates of civil rights and environmental rights who "clog" the courts with demands that the government obey the law.

Meese's lawyers, E. Bob Wallach of San Francisco and Leonard Garment, who represented Richard M. Nixon in the bizarre case of the 18 1/2-minute gap on the Watergate tapes, charged Meese at their usual rate, about $225 an hour. Delicacy, they say, precluded any discount -- they did not wish to be suspected of trimming their prices for a potential attorney general. But the size of the bill underlines the amount of time and high-priced effort required to prove that Meese is not a candidate for indictment.

It isn't as if Meese doesn't know the embarrassment that can be caused when a high official presents the public with a large legal bill. When former secretary of state Alexander M. Haig Jr. incurred $86,047 in legal bills from Joseph A. Califano Jr., a lawyer with a six-figure income who guided him through his 1981 confirmation hearings, the Reagan transition fund hastily stepped forward to pick up the tab. The administrator of "Transition Funds Inc." was none other than Meese.

Meese might have been well-advised to follow his own example. Reagan's rich friends would have been glad to kick in for a defense fund. If someone had passed the hat at one of the better hotels during the recent inaugural revels, Meese's debt could have been covered in a matter of hours.

A K Street lawyer who did not wish to be named because he expects to be doing business with Attorney General Meese within the next few months said, "It's a matter of bad judgment, and that's the real rap against Meese."

The attorney general-designate has not shown a particular sensitivity for public opinion. He made tactless remarks about patrons of soup kitchens, called the American Civil Liberties Union a "criminals' lobby" and once referred to nuclear war as "something that may not be desirable." His partisans say such obtusities arise from his desire to shield his patron.

The White House counselor, who, like the president, is an affable hard-liner, shares President Reagan's suspicion that poor people are always raiding the public treasury and taking advantage of the government. He and Reagan have a loathing for the Legal Services Corporation, which provides free legal help to those who, like Meese, cannot always pay their bills.

So far, Meese's $700,000 bill has not caused any outcry from the Senate Judiciary Committee, which is to begin Round 2 of Meese's confirmation hearings next Thursday. Republicans want to get the whole awkward business behind them. Few consider Meese the ideal "people's lawyer," but the argument for going along -- and it is also used by Democrats -- is the inevitability of his confirmation.

The Alliance for Justice, an organization of public-interest groups, has filed suit in the U.S. Court of Appeals here to open the sealed papers concerning the bill for Meese's legal fees. Common Cause, led by Chairman Archibald Cox, who was once an independent counsel, is ready to march, using the Stein Report as a field manual and Bible. Papers across the country have editorialized against Meese's nomination but have failed to arouse anyone with a vote in the matter.

The public might prefer a less expensive attorney general, and the Justice Department, which must offer the appeals court advice about paying his bills, might wish for a leader with a sharper sense of ethics and propriety. But Washington morality is that such yearnings were buried in the landslide of Nov. 6.