“[P]romote the general welfare” is an objective of the Constitution, but it is only achieved through the enumerated powers of the Constitution. Anything else is unconstitutional.
No matter what you and I think, most folks go along with the idea that Fed's have more powers than those specifically enumerated in Article 1. The word 'immigration' does not appear anywhere in the constitution, yet we go along with the idea that the power to set limits on immigration is an inherent power of congress for the president to enforce. There are a lot of other things that you and I would take for granted that are like that.
mho is that we need to use some judgment here case by case.