An anti-Shia coalition masquerading as a Middle Eastern security alliance will only fuel those sectarian fires and produce more, not less, terrorism. Instead of taking sides in that conflict, Washington should press Riyadh and Tehran to stop feeding it.

Second, whereas our core alliances in Europe and Asia are defensive, our Arab partners could use the anti-Islamic State coalition to go on the offensive, dragging the United States into new misadventures in the Middle East. Exhibit A is Riyadh’s counterproductive campaign in Yemen against the Houthi rebels, whom they see as an Iranian proxy.

I was the first senior American official to meet with Riyadh’s dynamic Deputy Crown Prince Mohammed bin Salman after the Saudi intervention in Yemen in 2015. I reiterated the United States’ commitment to defend Saudi Arabia against Houthi aggression and to help press the Houthis back to the bargaining table. Then I asked him Saudi Arabia’s objective in Yemen itself. “To remove every last vestige of Iranian influence,” he responded.

Two years and countless civilian casualties later, the Saudis are still at it, with Washington torn between backing our ally and being complicit in a fiasco that’s also leaving a power vacuum filled by the Islamic State and Al Qaeda in the Arabian Peninsula.

Third, while Mr. Trump expects a Middle Eastern coalition to leverage the Arabs to do more, they will want to use it to deepen United States military engagement in the Middle East, while doing as little as possible themselves. Mr. Trump’s frustration with spendthrift NATO allies in Europe will pale in comparison to what awaits him in the Middle East. The members of the existing mutual-assistance structure — the Gulf Cooperation Council — are risk averse, fearful of reprisals and divided in their priorities. They will spend more on weapons but are unlikely to use them effectively against the Islamic State.

Finally, NATO itself is more than a coalition of common interests — it’s an alliance of shared values. Mr. Trump seems more at home with Middle Eastern autocrats than he does with European democrats. Interests change and diverge; values do not. In their absence, an “Arab NATO” will prove to be a hollow enterprise.