I can't agree with this reasoning - there were many prejudices which started in different societies - prejudice against gays to name one. Just as homosexuality, prostitution violate religious norms and in most cases "real negatives" you mentioned, are nothing but people's internal feelings that this is something unethical to do.
In medieval christian Europe prostitutes were (together with the jews or the lepers) considered "unclean", forced to live in prescribed zones, and had a bad reputation. But they were usually "well tolerated" by even this most sexually repressive religion, as a necessary evil to prevent "worse sins" such as men having ex with married women, or unmarried virgin ones. So this view of the job as being useful, regulated (municipal brothels were a widespread thing), and something that were out people and everyone was embarrassed about, was as true then as it is now. This is what the current attempts at "normalizing" prostitution aim at, ironically. "Harm reduction" ,"empowerment", "preventing abuse", call it what you will... I see this this effort to re-brand prostitution as "sex work" is akin to the arguments among the high clergy about the usefulness of regulated brothels back in the middle ages. But perhaps I'm being too cynical?
The problem with this particular prejudice is that it just won't go away, unlike others that you mentioned. It has always been a job that marks people as outcasts in significant ways, It will always be a job that mark people as outcasts. It is intrinsic to the job: sex for money when most people who can have sex for free have it for free marks the clients as losers who are not good enough to get it for free. That makes it "shameful", even where it is legal and accepted as "normal". The "porn stats", the "high-end escorts", the "dancers", "masseurs", or "artists" will disguise it under a layer of glamor, but from what I've seen it always fails to stick: the clients remain ashamed to be knows as regulars of prostitutes. A trophy girl/boyfriend is one thing, a prostitute is another entirely different - even if both are actually in it only temporarily and for the money, and both know it: the important thing is that others don't actually know. The only kind of men (or woman) who brags about having prostitutes is the wealthy, still good-looking and supremely self-assured one who dismisses these prostitutes as objects, to be used because his time is too valuable to be wasted seducing someone while on a trip is something like that.
As for the prostitutes, most eventually leave the "industry" and will do their best to bury the past and let no one who interacts with them in the "new life" know of that past, even in the most liberal of societies where prostitution is legal and accepted. A few will stick with their "sex work" personas in a world that is unforgiving of the decays of age - thus the many suicides among those. I have an historic curiosity about the "porn industry" and have been noticing these things... rather sad.
Of course it is not a 'real' sex, just surrogate of it. But what makes it more demeaning and pathetic than, say, masturbation? And what makes it more 'lie' than porn movies (or any movies, for that matter)?
Masturbation is private (well, not necessarily

but you get what I mean). Everybody does it and knows about it, but people don't talk about it except to joke. It is politely ignored. Try bragging to your friends or colleagues that you masturbated in the morning and watch the looks afterwards... but if you brag about having had a nice night wink wink with your girl/boyfriend, or even a one-night-stand hookup, the reaction is entirely different.
Porn is also usually consumed privately. Everybody does it, sure. But this effort to keep it private does show that we are kind of ashamed of it, doesn't it? It is not the shame of something forbidden, it is the shame of something inadequate: those are replacements for the free sex with someone who actually desires to **** with you. Perhaps this shame should not exist - but it does. And I doubt it will change.
I'm struggling to understand how this differentiates prostitution from any other kind of service work.
I mean, baristas don't even get to work from home.
Baristas have no problem with letting it be knows they are baristas. Very few prostitutes announce their jobs outside of the job. The porn stars, basically, and you'll notice they still work under aliases even though now it's impossible to erase one's past.
Mind you, I do not disagree that there are many services works that are demeaning. Not do I like our current social organization where everything seems to be for sale. It is almost as if someone were trying to make this old prediction true:
Finally, there came a time when everything that men had considered as inalienable became an object of exchange, of traffic and could be alienated. This is the time when the very things which till then had been communicated, but never exchanged; given, but never sold; acquired, but never bought virtue, love, conviction, knowledge, conscience, etc. when everything, in short, passed into commerce. It is the time of general corruption, of universal venality, or, to speak in terms of political economy, the time when everything, moral or physical, having become a marketable value, is brought to the market to be assessed at its truest value.
"Sex work" is nothing new, I do know that... but at least in the past, and up till now, people acknowledged that it was a "necessary evil". Activists (and supposedly "left-wing" ones at that!) want to present it as some kind of virtue! Now that everyone chases perfection and love, it is sold wrapped up in that - perfect, professional sex. Be loved for one night, or one hour, or whatever. Even if everyone is onto the deceit. There are things that should not ever be sold nor even used for sales purposes.
In before anyone (everyone?) jumps on me for being "anti-liberal", I was giving a (rather long-winded) answer to Lohrenswald's original post. I can acknowledge that given poverty and inequality (and sometimes rather immature people), controlling prostitution is better than trying to ban it. What I do not like is the pretense that it should be presented as a good thing. It is a false pretense, one that can never be fulfilled.