There are only so many refugees and immigrants that we can take in each year which still requires a border patrol system.
You need to separate refugees from immigrants. This is US law, that people applying for refugee status have to be accepted until their hearing on refugee status. As I said it is not only international law, it is US law as well:
www.law.cornell.edu
(1)In general
Any
alien who is physically present in the
United States or who arrives in the
United States (whether or not at a designated port of arrival and including an
alien who is brought to the
United States after having been interdicted in international or
United States waters), irrespective of such
alien’s status, may apply for asylum in accordance with this section or, where applicable,
section 1225(b) of this title.
At the hearing the burden of proof is on the alien to show that he or she is a refugee, but until then, whether the person crossed the border legally or illegally has the right to be in the US. The person does not have a right to find a job. That can be limited. But that only puts a burden on the US taxpayers.