Clearly the federal courts (six different district courts, if I've counted correctly) don't believe that the case is as open and shut as you do, or they wouldn't have aisued restraining orders against the EO, one of the explicit considerationa for which is likelihood of prevailing on the merits.
That one section of law appears to be a broad grant of power does not mean that that grant is not constrained by other provisions of law.
(A) Except as specifically provided in paragraph (2) and in sections 1101(a)(27), 1151(b)(2)(A)(i), and 1153 of this title, no person shall receive any preference or priority or be discriminated against in the issuance of an immigrant visa because of the person’s race, sex, nationality, place of birth, or place of residence.
http://cdn.ca9.uscourts.gov/datastore/general/2017/02/06/17-...
My concern about the presidential order is that it bypasses due process and in this case may even be illegal. It appears it may not even have been shown to the administration's attorneys before implementation betrays a cavalier neglect for legality or the enormous harm this order has done to the reputation of the US as a fair country under the rule of law.