Except imagine that the FBI was in charge of issuing flags rather than sites, and the sites are given a short window of time to take the content down after it's been flagged
Yep, the good old FBI. They're really good at issuing flags appropriately. Never let shooters through. Never issue out NSL with indefinitely spans allowing warrantless searches that amount to nothing. Yep, I totally trust the FBI.
Meanwhile, back in reality, if there's actual sex trafficking going on, I don't want a website pulled offline. I wanted subpoena and/or warrants issued, those being trafficked rescued, and those doing the trafficking put in prison. I want most* websites to be functional honeypots, where people are investigated legally (without censorship laws), and then the ads just silently disappear because they're no longer relevant. Goodness, what was stopping the FBI from doing the above up until this point? A lack of resources?
Yep, the solution then is to give the FBI unilateral power to take down ads/web pages/web sites or...risk a punishment they can't be bothered/aren't capable of administrating? I guess they can leverage Google, Microsoft, or whoever to block the websites when they can't afford to do it or risk some sort of punishment...which they could probably have threatened before due to being some sort of co-conspirator and the general negative publicity of being associated with sex trafficking. Of course, this gives them a bigger threat club and the gray area is a lot bigger to swing it into, so double plus good for them.
* If you find a website that's explicitly** encouraging sex trafficking and/or makes no effort to block it but does block other content, there by making it pretty implicitly clearly they support sex trafficking, then yea, get them as co-conspirators.
** Not merely gray areas stuff will people conflate "Asian" with "must be human trafficking", "young" with "must be underage", or go by a list of "code words" that a lot of people don't know and wouldn't know to mean whatever the FBI says they mean. Sure, notify the people that you believe that's what's going on, but don't just presume everyone knows that "potato" means something special. Also, I really hope potato doesn't mean anything.