Arty, the 4 your noted are Islamic Maghreb, but Americans wouldn't know much of a distinction, nor care. Many are unfamiliar differences between the Arab world and the Muslim world.
DJT certainly would love to have a "complete and total shutdown of Muslim" immigration if he could. But they know the backlash would be un-containable. The 3 aforementioned countries, as I stated, could hit back in retaliation. Example would be Egypt could go and refuse to work with Israel on numerous important issues like Yemen. Tel Aviv would then call Washington and relay the dismay. Jordan no doubt is providing humint to the DoD on subjects like Hezbollah. Turkey would throw a fit and call NATO into question.
(Indonesia might be the nation with the largest Muslim populace but for the longest time it's action is not Muslim-world centric, but Asia-centric.)
Let me quote you guys some from Section 1 of the ban, aka statement of purpose:
Perhaps in no instance was that more apparent than the terrorist attacks of September 11, 2001, when State Department policy prevented consular officers from properly scrutinizing the visa applications of several of the 19 foreign nationals who went on to murder nearly 3,000 Americans. And while the visa-issuance process was reviewed and amended after the September 11 attacks to better detect would-be terrorists from receiving visas, these measures did not stop attacks by foreign nationals who were admitted to the United States.
Numerous foreign-born individuals have been convicted or implicated in terrorism-related crimes since September 11, 2001, including foreign nationals who entered the United States after receiving visitor, student, or employment visas, or who entered through the United States refugee resettlement program.
Here is a list of the attacks on US soil since 9/11:
2016 Omar Mateen shot dead 49 at the Pulse nightclub in Orlando. His parents were originally from Afghanistan. He was born in New York.
2015 Syed Rizwan Farook and his wife Tashfeen Malik shot dead 14 people at an office in San Bernardino, Ca., before they were killed. He was born in Chicago to parents from Pakistan. She was born in Pakistan and raised mostly in Saudi Arabia.
2015 Mohammad Abdulazeez opened fire at two military recruiting centers in Chattanooga, Tenn., killing five U.S. military personnel. He was a naturalized American who was born in Kuwait to parents who were Jordanian and Palestinian.
2013 Two brothers, Tamerlan and Dzhokhar Tsarnaev carried out the Boston Marathon bombing that killed three. Tamerlan was born in the Soviet Union (now southern Russia), and Dzokhar was born in Kyrgyzstan.
2009 Army Maj. Nidal Hasan, shot dead 13 in Ft. Hood, Texas. Hasan, who was born in Virginia to Palestinian parents who had immigrated from the West Bank, has been sentenced to the death penalty.
2009 Abdulhakim Muhammad shot and killed an Army private at a recruiting center in Little Rock. He was born in Memphis to a Christian family, but converted to Islam and changed his name from Carlos Bledsoe.
2002 Egyptian national Hesham Hadayet shot dead two Israelis at the El Al airline ticket counter at the Los Angeles Airport before being killed.
If the WH can't square the stated purpose and the actual evidence, then order they give has no merits.