It may sound like I'm trying to jerk your chain, but I'm not. I am, however, going to jerk the Supreme Court's chain a little.
The Supreme Court said the following about the Tenth Amendment: "More specifically, '"the Framers of the Constitution intended the States to keep for themselves, as provided in the Tenth Amendment, the power to regulate elections."'" That's it. They did not find any violation of the Tenth Amendment, that I can see, nor did they specifically state in Shelby County that "equal sovereignty" was based upon that Amendment.
On the contrary, "equal sovereignty" was based upon case law. As Justice Ginsburg pointed out, "In Katzenbach, however, the Court held, in no uncertain terms, that the [equal sovereignty] principle 'applies only to the terms upon which States are admitted to the Union, and not to the remedies for local evils which have subsequently appeared.'"
The majority, taking a passage from the Northwest Austin case (a passage that Justice Ginsburg calls "dictum"), says that equal sovereignty "remains highly pertinent in assessing subsequent disparate treatment of States." But is there a body of law that supports this conclusion? Are there a set of standards for applicability of the principle, as there are when disparate treatment of humans is concerned? No, there are no such standards in the case law.
Or in the Constitution.
Again, I don't want to go into this too much; but it is odd that a group of five justices who hold themselves out as relying upon the text of the Constitution when deciding whether a statute is unconstitutional seemed to rely on a doctrine that was not expressly founded in the text of the Constitution.