Because "their guy" said exactly what he would do, and it is ugly.
Compare to the implicit scopes of the 4th Amendment, which I'll quote in full:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
Many have argued that these pervasive dragnet surveillance systems axiomatically violate the 4th Amendment by their scope alone ("particularly describing the place to be searched, and the persons or things to be seized"), which akin to the much, much greater scope of WMDs vs. the arms of infantrymen.
Although this domain is a lot more nuanced, e.g. metadata is pretty universally held not to be protected like data, but what about mass collection of metadata?
What makes the US Government so special that it should be armed with world-ending nuclear weapons? How is a large bureaucracy somehow better than say a private corporation or even an individual in that regard? There is no answer...
It's certainly a serious argument for a strong, in this domain, serious central government. I don't think anything in federalism besides the usual political stuff applies.
And that "usual political stuff" is where this government gets it moral legitimacy, which partly addresses your point, especially when we strip away ludicrous hyperbole like "world-ending" (maybe your world would end, but things would remain largely unchanged for perhaps half the world's population, and not severely changed for a very large fraction of the rest; the world is big, and we are small).
And while "might makes right" might not settle well with your moral tastes, operationally, might rules. Otherwise, you might be counting yourself lucky to be speaking Russian. But not needing to speak Punic.