The 4th Amendment in practice, as really any law, cannot preemptively stop the bad practices of actors working in bad faith. It's remediative, as in, the evidence it collects at least in theory cannot be admitted as evidence in court. If you look at indictments, informations, any initial charging document, you'll see at least some if not a deluge of blatantly inadmissible or dubiously obtained pieces of information that makes up probable cause. This is a feature of the system, and also why you don't plead guilty on the information alone (in state and federal felony practice I've seen 1 person plead guilty on the indicting information, he was pro se, this was 2013). Superseding indictments frequently look nothing like the original. Call it cynical, or pragmatic, but in 20% of the states - including some of the larger states like New York, Washington, Michigan, Ohio, Wisconsin etc. - it's not merely allowed and common for cases to end up with a plea that contains charges that have no factual basis linkable to the allegations first presented because we know what the game is and it's not about justice or public safety, it's about retribution, on someone lower on the totem pole. The evidence becomes secondary because the system incentivizes it. The 4th Amendment of course covers more than that, and if we simply reverted the interpretation back to the text we'd be doing much better.
Sadly it has been whittled down and have not caught up with tech - it's a lagging indicator at best. Things like the third party doctrine, automotive exception, pretext stops, etc. are things that should enrage anyone who cares about the most fundamental rights we have not just as Americans but as people, individuals, private persons, who are fundamentally equal to each other if not in circumstance but at least in substance. The courts sometimes even mis-states their own doctrine and usually in favor of the state. Why is there no good faith exception the other way? Any idiot can see that the plain view doctrine opens a pandora's box. We don't need the NSA for our rights to be handwaved away, that's already done.
The NSA does not testify in open court, and we can only speculate what they are able to really launder down into the criminal justice system. But considering that the state of the 4th Amendment have already made the system extremely coercive with limited recourse in so many "exceptions" that are no where near the intent of the framers of the Constitution and frankly tilts the ice more than any crooked lower league Russian Hockey match, it's likely not even necessary for them to jump in most of the time.
I suspect that the greater influence they exert is through the military-industrial complex in its modern day form. We're the only country that can just waltz in and invade.. what, 7, 8 countries? Has anyone been to China lately and have the connections to assess the state of their military and economy with clear eyes? Do people see the laundering of BS national security concerns into reputable papers and conspiracy rags alike? It's usually innocuous sounding, but no small part of the economic quagmire comes from the continued funding, justified by the agencies that are the constituency with a vested interest, of this pit of unaccountable money. We'll be paying for it either way, because not enough people care, unfortunately.