The snowden leaks revealed that's not the case.
The three letter agencies can just issue national security letters without a judge ever seeing it, and those come a long with a gag order (plus other workarounds like just buying data from brokers, and how US communications can get swept up just by virtue of communicating with a foreign national outside the US).
You're right, they aren't omniscient in the way we imagine of a room full of people monitoring everything in real time. But to pretend they aren't passively collecting massive amounts of data is dangerous. Snowden showed us PRISM, with all major tech companies participating. They do effectively have a live, unrestricted wiretap to the internet and if you happen to be a person of interest, they will just send out NSLs and get all your communications that are not fully E2EE without you even knowing thanks to the gag order.
I'll provide some helper information to get the ball rolling (see page 42)[1]
[1]https://www.intelligence.gov/assets/documents/702-documents/...
All the other prime suspects are in the report too for the curious.
I will not elaborate how I know, but that is not even directionally correct. But these are not even secret things that can’t be known simply through the Snowden, Wikileaks, and Vault7 releases. So why are you telling yourself this? Are you still wet behind the ears or something?
There are people who know exactly how governments do not in fact need warrants and the tech companies don’t even really know they are servants to the government, let alone which one. That’s how things are done. The less surface area the better.