There are lots of things wrong with this defense.
First, it doesn't match up with U.S. law. Wiretapping is legally defined as acquisition by device, with no requirement that a human look at it. This has been the case since 1968, amended in 1986.
Second, it's unconstitutional. The Fourth Amendment prohibits general warrants: warrants that don’t describe "the place to be searched, and the persons or things to be seized." The sort of indiscriminate search and seizure the NSA is conducting is exactly the sort of general warrant that the Constitution forbids, in addition to it being a search by any reasonable definition of the term. The NSA has tried to secretly redefine the word "search," but it’s forgotten about the seizure part. When it collects data on all of us, it’s seizing it.
Third, this assertion leads to absurd conclusions. Mandatory cameras in bedrooms could become okay, as long as there were rules governing when the government could look at the recordings. Being required to wear a police-issued listening device 24/7 could become okay, as long as those same rules were in place. If you're uncomfortable with these notions, it's because you realize that data collection matters, regardless of whether someone looks at it.
Fourth, creating such an attractive target is reckless. The NSA claims to be one of the biggest victims of foreign hacking attempts, and it’s holding all of this information on us? Yes, the NSA is good at security, but it’s ridiculous to assume it can survive all attacks by foreign governments, criminals, and hackers—especially when a single insider was able to walk out of the door with pretty much all their secrets.
Finally, and most importantly: Even if you are not bothered by the speciousness of the legal justifications, or you are already desensitized to government invasion of your privacy, there is a danger grounded in everything we have learned about how humans respond when put in positions of unchecked power. Assuming the NSA follows its own rules—which even it admits it doesn’t always—rules can change quickly. The NSA says it only looks at such data when investigating terrorism, but the definition of that term has broadened considerably. The NSA is constantly pushing the law to allow more and more surveillance. Even Representative Jim Sensenbrenner, the author of the Patriot Act, says that it doesn’t allow what the NSA claims it allows.
A massive trove of surveillance data on everyone is incredibly tempting for all parts of government to use. Once we have everyone’s data, it’ll be hard to prevent it from being used to solve conventional crimes and for all sorts of things. It’s a totalitarian government's wet dream.
The NSA’s claim that it only looks when it’s investigating terrorism is already false. We already know the NSA passes data to the DEA and IRS with instructions to lie about its origins in court—"parallel construction" is the term being used. What else is done with that data? What else could be?