Reacting to the mixed reviews of Secretary of State Alexander Haig's on-the-scene inspection of the problems confounding coherent American policy in the Middle East, a seasoned, well-respected student of the subject very nearly shouted the other day:

"Why is it that with every new administration we have to re-invent the wheel?"

The "wheel" in question, to be sure, is an extraordinarily complicated and delicate piece of machinery. It can't run on dogma or grand strategy. For it to work at all requires sober, steady recognition of all the political, military and economic forces at work in the area stretching from Israel to the Persian Gulf, now broadened by the Reagan administration's grand designers to include Turkey, Pakistan and Afghanistan.

Solutions are always fiercely controversial, and easy prey to partisan politics; hence a powerful impulse at the start of any new administration to innovate. Richard Nixon tried studied neglect until the area exploded into the October 1973 Arab-Israeli war. Only then did he turn to the hard business of Henry Kissinger's shuttle diplomacy.

Jimmy Carter, thinking bug, went for the sweeping "comprehensive" solution by trying to bring the Soviets into the act. That backfired by outraging the Israelis. But it also encouraged the breakthrough in Jerusalem that lead to the considerable, though more modest, Camp David breakthrough.

Thinking even bigger, the Reagan administration came on strong, initially, with an approach that seemed to shove the Arab-Israeli conflict aside, as a matter of secondary importance to what an official State Department spokesman was describing, in advance of the Haig tour, as "the deteriorating position of the West vis-a-vis the Soviet Union." The East-West element was to be given "the highest priority in that region at this time."

But just recently, after Haig's return, that same spokesman was insisting to me that the secretary "doesn't set one priority higher than any other. He believes that East-West security concerns and the Palestine issue are mutually reinforcing, that you can't make progress without making progress on both." That, he added, had been Haig's view all along.

Why quibble? If that is the State Department's view, the "re-invention" process is under way in what strikes me as an encouraging fashion. Immutable facts of life -- Israel's support for the Camp David process, Saudi Arabian preoccupation with Jerusalem and the Palestinian cause, King Hussein's disinterest in a "Jordanian option" for dealing with West Bank occupation by Israel -- are beginning to sink in.

In those terms, Haig's inability to establish in any public way a "strategic consensus" on the Soviet menace is only a failure in the sense that in the advance billing he may have needlessly set himself up for a fall. As one wise Arab diplomat put it, "He had his strategic consensus all along, if by that you mean that there is general agreement, at least among the Saudis, the Egyptians, the Jordanians and the Israelis of a Soviet threat. The only way he can lose it is by talking about it so much."

If that lesson had indeed been learned, then you could count the Haig inspection trip as a success -- as the State Department clearly does. The secretary, they insist, was cordially received; he struck up good working relations with the top people in the four countries (Egypt, Israel, Saudi Arabia and Jordan) that he visited. The private talks went much more smoothly than some of the public disclaimers of his Arab hosts suggested.

But there remains disturbing evidence that however much Haig's hand may have been strengthened in the fashioning of realistic and workable Middle East policy for the Reagan administration by his face-to-face encounters, the "re-invention" process still has a distance to go. f

The evidence is to be found in a general tendency, centering in the White House and in the president himself, to cling hard to the concept of the East-West conflict as the overriding Middle East concern to the virtual exclusion of the Palestinian issue. The president, according to reliable sources, still thinks -- and startles visiting foreign dignitaries by talking -- of the Palestinians as "refugees," as he was wont to do in last year's campaign.

But Exhibit A in the evidence of misplaced emphasis on military presence and military solutions to deter the Soviets is nowhere more alarmingly demonstrated than in the administration's apparent determination to sell enormously sophisticated, commanding-control, early-warning AWACS aircraft to Saudi Arabia. The Israelis, says an official, will oppose this enhancement of Saudi air power "with all our vehemence." A rough, probably losing, fight looms for the administration in Congress.

Either way it turns out -- Israel enraged or Saudi Arabia denied -- is a poor way to advance the process of "re-inventing" an effective approach to Mideast policy.