Yes, the U.S. Senate appears about to modify the section of the CDA (Communications Decency Act - 230) to expressly carve out websites that facilitate sex trafficking from section 230's immunity, which would then allow prosecutors to target websites that "facilitate sex trafficking."
Of course, prosecution doesn't necessarily mean criminal convictions, but the mere threat of prosecution is liable to cause changes in the websites, and, even more so, actual prosecution causes potentially huge defendant legal expenses.
All that said, whatever happens in Congress (and the House of Reps has a similar bill pending as well) and whether the bill(s) are signed into law means future legal processes in the Federal courts must also come to bear on websites.
Websites, by the way,
which are not hosted in the U.S. can obviously still be targets of prosecutors, assuming that the corporate entities are U.S. based. A website owned and hosted offshore might still be targeted, assuming that the host country accepts and cooperates in the prosecution.
BackPage.com appears to be the main target of the congressional efforts, plus many of the other websites (including dating websites) that appear to be facilitating underage and sex trafficking operations.
Just curious, I am, how many FaceBook accounts support providers? I only know of a couple dozen personally, and only because those providers have sent me links. I don't search FB for hookups, but extrapolating from the dozens I know about there must be hundreds more if not thousands.
Reality check:
imo, no matter what the legal efforts might entail, the "web" is so broad and pervasive that legal efforts will be largely unsuccessful and most often trying to catch up to new technology such as twitter, snapchat tinder, etc. increasingly channel "sex" hookups on a commercial basis.
The OP's thoughts are valued here, and my caution to all involved in the Hobby is that the true value in communications suggests that multiple backups are necessary in order to keep communications channels alive and well.