To repeat: In Title 8, U.S. Code (which is where the immigration laws are), sec. 1225(b)(1)(B)(IV) states:

Any alien subject to the procedures under this clause shall be detained pending a final determination of credible fear of persecution and, if found not to have such a fear, until removed. [Emphasis added]

That is the presumptive rule. Even aliens who may have a valid “fear of persecution” claim are supposed to be kept in custody until that claim is adjudicated. They are not to be released into the United States. That is a congressional statute, and there is no plausible claim that it is unconstitutional. Therefore, the president’s sworn duty is to execute it faithfully.

So, that’s what the law says: Aliens who are apprehended trying to enter our country illegally are supposed to be detained.