How can you verify whether an account belongs to a US citizen without possessing a single bit of data about it?
>if the company receiving the wiretap order has any reason to believe that an account belongs to a US citizen or a non-US citizen living in the US, they challenge the order
Correction: the company can challenge the order. In case you've been living under a rock / off the grid and haven't seen the Twitter files recently, private companies not only aren't fighting back against government spying, censorship, etc - they're openly cooperating, going so far as to set up task forces to facilitate open cooperation. Why do you think Microsoft was feeding PRISM 5 years earlier than Apple? It's not like one organization had vastly more technical capability than the other - some private organizations are just openly complicit with the government regardless of the morality. IBM produced many of the systems used by the Germans to facilitate the holocaust - something being legal and profitable doesn't inherently make it morally acceptable.
>by all accounts, including Snowden's documents, that procedure is followed.
It is followed in the letter of the law, not the spirit of the law, by a court that rubber stamps 99.97% of requests. Besides, as I've argued above, immoral actions should not be tolerated simply because they are allowed by law. See also: slavery, usury, civil asset forfeiture, murder of unarmed civilian by cop ft. qualified immunity, drone bombing weddings overseas, overthrowing democratically elected leaders in other countries, plotting fake terror attacks against US citizens to justify foreign wars (operation Northwoods).
Evil is evil regardless of whether or not it's been "made legal" by a corrupt government with an extensive track record of violating international sovereignty, human rights, the geneva convention, and arms control charters, not to mention the only country to ever commit genocide of civilians with an atomic weapon. The US has zero moral authority.