Trump promised in his campaign that he would ban Muslim immigration, because radical Islamic terror. Someone apparently got through to Trump that a Muslim ban wouldn't pass constitutional muster, so the ban was "tailored" as an emergency ban for the purposes of terrorism.

If you look at the mass casualty incidents since 9/11, only at best ~50% of them were instigated by immigrants, let alone Muslim immigrants. A leaked DHS report apparently concludes that even most of those immigrants who did commit terrorism were radicalized post-entry, although this should have been the reasonable assumption of anyone who cast a cursory glance at the evidence.

The exclusion of Saudi Arabia, Egypt, UAE, Pakistan, and now Iraq, as well as the inclusion of Iran on the list (Iran's support of terrorism is pretty much limited to proxies whose targets are limited to Middle Eastern governments (including Israel) and have no inclination to carry out attacks in the US or Europe) indicate that the set of targets is chosen less for which countries are liable to produce terrorists and more for which countries the US government doesn't like.

As I've pointed out in the past, the number of terrorists who might be stopped by a travel ban like this is probably 0 and maybe as high as 2. The number of people for whom this would be the tipping point in their radicalization is probably between 0 and 10. This may create more terrorism than it catches.