> US immigration law gives the president explicit right to do exactly what he did

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.