No, the clause simply allows the feds to make a uniform rule for the criteria that must be met in order for someone to become a citizen.
They do NOT have the ability to decide who may or may not be a citizen.
It's a fine line, but an important one, IMHO.
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The problem is the usage of the term 'immigrant'. Unless someone comes to this country and applies for citizenship, they are not an immigrant, but a denizen.
Denizens fall under the jurisdiction of the State where they reside, NOT the federal government.
From the first legal treatise written after Ratification:
The common law has affixed such distinct and appropriate ideas to the terms denization, and naturalization, that they can not be confounded together, or mistaken for each other in any legal transaction whatever. They are so absolutely distinct in their natures, that in England the rights they convey, can not both be given by the same power; the king can make denizens, by his grant, or letters patent, but nothing but an act of parliament can make a naturalized subject. This was the legal state of this subject in Virginia, when the federal constitution was adopted; it declares that congress shall have power to establish an uniform rule of naturalization; throughout the United States; but it also further declares, that the powers not delegated by the constitution to the U. States, nor prohibited by it to the states, are reserved to the states, respectively or to the people. The power of naturalization, and not that of denization, being delegated to congress, and the power of denization not being prohibited to the states by the constitution, that power ought not to be considered as given to congress, but, on the contrary, as being reserved to the states.
St. George Tucker
I don’t disagree with you, but I don’t see any real distinction between your phraseology and the one I chose instead.