It is wrong to think of immigration primarily as a problem to solve—as an “it” when it is really a “he,” “she,” and “they.”
Regarding my doubts that the Congress has a general power to regulate immigration, some observers, including Ken Masugi, have noted the provision in Article I, section 9 providing that “The migration or importation of such persons as any of the states now existing shall think proper to admit, shall not be prohibited by the Congress prior to the year one thousand eight hundred and eight.” The suggestion is that this provision would not have been necessary, as to “the migration of persons,” if Congress lacked authority to regulate immigration.
But notice that my post suggested that Congress does have certain authority over immigration, just not general authority. Thus, Congress can regulate certain aspects of immigration that constitute foreign commerce. Similarly, Congress can prohibit immigrants entering the country through federal territories. So this provision is not inconsistent with my argument.