At any rate, Pompeo is right about the chaos that will follow, but it would be wrong to blame it all on Trump.
Turkey's President Recep Tayyib Erdogan is much better informed than the American president and probably a lot smarter too, but he is just as impulsive, just as ruthless, just as much a bringer of chaos.
It was Erdogan, in a telephone conversation in mid-December, who persuaded Trump that pulling all the US troops out of Syria would be a good idea. Turkey would be happy to take the strain instead.
Trump has always opposed America's endless Middle Eastern wars, so he swallowed Erdogan's suggestion hook, line and sinker — and tweeted his decision to pull the US troops out without discussing it with anybody.
Only later did the remaining grown-ups in the White House explain to him that Erdogan planned to subjugate or kill America's main allies in Syria, the Kurds.
To his credit, Trump hated the idea of betraying the Syrian Kurds, whose militia, the People's Protection Units (YPG), suffered thousands of deaths while helping US forces to defeat the fanatical jihadis of Islamic State.
Trump still wanted to bring the US troops home, but now he had one condition. The Turks must promise not to invade northeastern Syria and crush the YPG when US troops leave.
Erdogan replied that nothing Trump said or did could stop him from destroying these Kurdish "terrorists" (who have never attacked Turkey). At which point, last week, Trump tweeted that the United States "will devastate Turkey economically if they hit Kurds."
All clear so far? Good.
You'd never guess, from the story thus far, that the United States and Turkey have been close allies for the past half-century, but the alliance is fading fast. Erdogan has been playing his own hand in the Middle East, and playing it quite badly.
The "Sultan", as his admirers call him, wants to secure his own one-man rule and re-Islamise Turkey, which had evolved into a secular and democratic republic.
He also wants to promote Sunni Islam throughout the region. The two goals are not fully compatible, so he shifts position a lot.
When the revolt in Syria broke out in 2011 during the Arab spring, Erdogan supported it because Bashar al-Assad's regime is dominated by Alawites, a Shia Muslim sect.
When Russia intervened militarily to save Assad in 2015, Erdogan was so angry he had the air force ambush and shoot down a Russian bomber. But he was almost equally angry with the United States, which had made an alliance with the Kurds of northern Syria to fight Islamic State.
The Kurds gradually choked off the aid coming in to Islamic State from Turkey, and IS (aka "Isis") has now lost almost all its territory.
So Erdogan told Trump he could bring the US troops home now, and Trump believed him. But what Erdogan actually wants to do is crush the Syrian Kurds, which he can do once the US troops leave.
Erdogan thinks the Syrian Kurds are allied with the Turkish Kurds, who make up one-fifth of Turkey's population, live just across the border from Syria, and are currently at war with Erdogan's regime (that's why he calls them "terrorists".)
The weird thing is that four years ago Erdogan was on the brink of making peace with the Kurds. There was a ceasefire, the Turkish Kurds were no longer demanding independence, and he was negotiating a compromise settlement that enhanced Kurdish rights within Turkey.
But then he lost a parliamentary election in 2015, mainly because the Kurds stopped voting for him. So he re-opened the war against the Kurds, wrapped himself in the Turkish flag, and won the next election on an ultra-nationalist platform.
All Kurds are now the enemy, they are all terrorists, and they must be crushed.
Given Erdogan's ruthlessness and Trump's volatility, I have no idea how all this works out ... badly, I suspect.
But I admire Trump's refusal to betray his allies, once he realised what Erdogan was up to. You don't see that much in the Middle East.
Of course, it probably won't last.
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Gwynne Dyer's new book is Growing Pains: The Future of Democracy (and Work)