Meanwhile, SESTA/FOSTA effectively puts such a burden on web operators that even legitimate sites (like Craiglist personals) have been shut down out of fear that they will be liable if someone misuses them. This is even true in states and municipalities that choose to legalize prostitution. The effect of SESTA/FOSTA is to usurp states' ability to decide for themselves how they want to regulate the sex trade, at least as far as it comes to the communication platforms they can use. If the intent of SESTA/FOSTA was to inhibit prostitution that didn't involve trafficking, fine, but that's not how it was sold by elected Democrats.
I wouldn't be so cynical about this, except that there is a long history in the US of using moral panic around trafficking to enforce moral preferences -- look at how the Mann act was used against interracial couples, for example. I'm all for helping actual victims of trafficking, but using outrage about trafficking for other political purposes upsets me.
Alternately, decriminalizing sex work means law enforcement would stop wasting their time their pursuing adult sex workers doing legit business, and actually focus on the trafficking of those actually being exploited.
The majority of people oppose decriminalisation [1] even in fairly progressive Ontario, Canada, 6 in 10 oppose it [2]
Second - it's a very reasonable course of action to make an activity which is deemed harmful - actually illegal.
"Smoking is bad" -> "Let's make it widely available" is generally not the first order course of action.
Ergo - your assumptions about 'moralising and not caring' is starting to inch into anti-religious bigotry territory.
Now - obviously this is a nuanced issue - and it's possible more permissive laws might lessen harm, but this is by no means obvious.
We saw this with vaping: once something becomes socially normative, behaviours can grow rapidly. There is a black market for almost everything, legal or not.
A large, wide open, legalised & regulated sex trade may simply provide more customers for nefarious sex-traders who can take all the profit & provide underage girls (which will surely remain illegal).
The cigarette industry provides good parallel example, although it's surely not perfect. [3]
In short - increased taxes (i.e. supply curve shift) and overall changes in social norms away from smoking have not caused an increase in illicit consumption - just the opposite. Illicit consumption is down. This might imply that creating more barriers to the sex trade (law), and also reducing demand (social norms), would likely have the overall effect of reducing black market for sex-slavery.
Of course, it's not nearly a perfect analogy, and it's a complicated subject and of course there are individuals and groups who are probably more concerned about morality than justice, but it's still not fair to castigate a policy as being one way or the other.
Personally, I don't see how normalising the sex trade and providing vast online services decreases frequency of transactions, but I'm open minded about the right way to do this. Though I personally think it should be 'decriminalised' (not illegal, but sex workers not allowed to go to 'job fairs' at high school!), I would put the wellbeing of those being trafficked ahead of any of that.
[1] https://prostitution.procon.org/view.resource.php?resourceID...
[2] https://www.ipsos.com/en-ca/news-polls/LAWC-and-CATW-Prostit...
[3] https://tobaccoatlas.org/topic/illicit-trade/