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Mr. Pompeo’s trip is intended to underscore that far from fading out of the Middle East, the U.S. is leading a broad coalition against Iran. The linchpins of the effort are Israel and Saudi Arabia, which share a fear of Iranian expansionism and are the closest U.S. allies in the region. They have maintained informal but not-so-secret contacts, sharing intelligence on their common nemesis. Why not make it official?

A Netanyahu-Mohammed meeting would be a capstone of the Trump administration’s effort to isolate and contain Iran. The so-called Arab Street’s indifference to the U.S. Embassy’s move to Jerusalem is said to have given the crown prince the confidence to take his relationship with Israel public at the right time. On a more political level, it surely would divert public and media attention from problems currently besetting each of the three leaders involved.

For President Trump, it would be a respite from arguments over the government shutdown and his abrupt decision to withdraw from Syria. For Mr. Netanyahu, facing domestic political problems and a new election, it would be a dramatic breakthrough on the order of Anwar Sadat’s 1977 visit to Jerusalem. And for Crown Prince Mohammed, it could restore some of his international luster, tarnished by the Khashoggi murder (in which the Saudis insist the crown prince had no involvement).

Such a meeting would offer only upsides for Messrs. Trump and Netanyahu. For Crown Prince Mohammed it would entail some risk. Openly cooperating with Israel without resolving the future of Jerusalem and its Islamic holy sites surely would provoke opposition from religious Saudis, though only sotto voce given the crown prince’s severe repression of domestic opponents. On balance it would appear he has achieved an international success without domestic repercussion.

For two years Mr. Trump’s son-in-law, Jared Kushner, has worked to unite Israel and Saudi Arabia in a Mideast peace deal, ideally including full diplomatic relations. It isn’t clear the two countries are ready to go that far, but it does seem likely they are ready to leapfrog the intractable Palestinian issue and publicly cooperate with the U.S. to bring Iran to heel. Tehran’s growing influence in Syria, Lebanon and Yemen, and its intention to possess missiles that could reach the U.S., raises new alarms that militate in favor of a public Saudi-Israeli embrace.

Crown Prince Mohammed has been dropping hints that a formal rapprochement may be in the offing. On his April visit to the U.S., he publicly said when asked that the Jewish people, like “each people, anywhere, has a right to live in their peaceful nation.” Then he offered an Islamic justification: “Our Prophet Muhammad married a Jewish woman.” (A skeptic might note that before marrying the Jewish widow Safiyyah bint Huyayy, the prophet required her to convert to Islam.)

Until recently a public meeting between Israel’s prime minister and Saudi Arabia’s de facto ruler would have seemed impossible. Then again, so did the Sadat visit, President Nixon’s 1972 trip to China, and Mr. Trump’s summit with North Korea’s Kim Jong Un last year. New reality often sweeps away the logic of impossibility. And Mr. Trump loves spectacles. Imagine him watching the historic drama on television—or flying to Riyadh to join it.

Ms. House, a former publisher of The Wall Street Journal, is author of “On Saudi Arabia: Its People, Past, Religion, Fault Lines—and Future” (Knopf, 2012).