Citizenship and the 14th Amendment

Recently, as part of the whole immigration mess, some Republicans are looking at revising the 14th Amendment.  Specifically where it discuss "birthright citizenship."  They might do themselves a favor and actually look up some Constitutional precedents before being so hasty in changing the Constitution.  I'm getting this information from Wikipedia and it discusses the 14th Amendment birthright clause as it pertains to illegal immigrants.  Again, from Wikipedia:

The Supreme Court has never explicitly ruled on whether children born in the United States to illegal immigrant parents are entitled to birthright citizenship via the 14th Amendment,^[5] although it has generally been assumed that they are.^[6] A birth certificate issued by a U.S. state or territorial government is evidence of citizenship, and is usually accepted as proof of citizenship.
In the case of United States v. Wong Kim Ark, 169 U.S. 649 (1898), the Supreme Court ruled that a person becomes a citizen of the United States at the time of birth, by virtue of the first clause of the 14th amendment of the Constitution, if that person is:

• Born in the United States
• Has parents that are subjects of a foreign power, but not in any diplomatic or official capacity of that foreign power
• Has parents that have permanent domicile and residence in the United States
• Has parents that are in the United States for business

So, in fairness to these Republicans, it is generally assumed that a child of illegal immigrant parents would be granted citizenship.  However, this has never been tested.  Jeff Sessions had the following comment in the article,

"I'm not sure exactly what the drafters of the (14th) amendment had in mind, but I doubt it was that somebody could fly in from Brazil and have a child and fly back home with that child, and that child is forever an American citizen."

In the one case cited above, there are several conditions that must be met.  One involves permanent domicile and residence, the other for business reasons.  I would think it difficult for truly illegal immigrants to gain residence and if they have legitimate business reasons, they are probably here on work visas and therefore, not illegal.  I doubt Sessions was aware of the legal precedent.  I would be curious to see those citizenship rights challenged for the example he gave.

I am curious to see how this one plays out.  Based on the information available to me today, I have to say that it wouldn't kill me to see something change specific to this birthright clause.  The birthright clause reads as follows:

All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.

That last section of the 14th Amendment is a follows:

Section 5. The Congress shall have power to enforce, by appropriate legislation, the provisions of this article.

Laws have been passed to establish the rules by which territories and other U.S. entities are entitled to citizenship.  Based on Section 5 and the meaning of "subject to the jurisdiction thereof,"  I'm wondering if Congress could not first pass a law denying illegal immigrant birthright citizenship with the aid of Wong Kim Ark first and see if it stands up to the Constitutional challenge.

I also question the need for such an effort because I would think the percentage of birthright citizenship in comparison to the entire illegal immigrant issue is very small and may not really be worth it.  Certainly, I don't think it is nearly as important as dealing with our ongoing economic struggles and large scale illegal immigration issues.