Basically your post, taken at face value, consists of two question. The first one
Can anyone make a reasonable case why prostitution should be illegal while pornography is legal?
is similar to what gets posted on Reddit's “Change My View” – but guess what, some views are just flat out flawed, wrong, absurd, fatally inconsistent. It has no value to concoct a pseudo-reasonable case for such views.
If we look at the current US (excluding Nevada) legislation:
you'd have a Mount Everest to climb to get to a convincing-sounding justification.
Now to the most obvious concocted pseudo-justification, from an answer a Quora poster gave, to which user Pacerier linked here in a comment:
A third party is paying them both, but that third arty is not purchasing sex. That third party is buying their labor in the service of making a movie. The money or other material consideration is being exchanged for the end product of a motion picture, not for sex.
About two to three times a month, someone will come into Quora and ask “Can I hire a porn star to have sex with me and say I'm making a movie, but then just never release the movie, and that won't be prostitution?” And the answer is no. People have tried that. The courts won't accept that argument.
yeah … only that it is not uncommon that the producer also stars (= has sex) in the pornographic movie! This itself is not illegal.
The “third party pays” criterion is a figment of the non-lawyer's imagination!
Also, even if it were true, does it matter? If well-meaning uncle Bob pays a prostitute for his nephew Dave because he is a virgin at 20, it would still be illegal. So the only way out of this really is to claim that filming and publishing an act, which is criminal otherwise, magically makes it legal. And this is patently absurd.
Courts will “see through it” … yeah, but not on any remotely objective standard. It's just the very vague gut feeling of the prosecutor (and later the judge or jury) that a certain pornographic movie production seems just a bit too phony.
Okay, maybe we can look at the harm their work does to real pornographic actresses and prostitutes? But here it doesn't seem much better…
“Sexually Transmitted Infection Testing of Adult Film Performers: Is Disease Being Missed?” by Rodriguez-Hart et al. in Sexually Transmitted Diseases: December 2012 - Volume 39 - Issue 12
comes to the conclusion:
Compared with the brothel workers of Nevada, another legal sex worker population in the United States, GC [Gonorrhea] and CT [Chlamydia] prevalence in this study [of pornographic actors in Los Angeles, CA] is significantly higher. […]
The high prevalence of STI infections and the discordance between anatomical sites are especially concerning because the potential for rapid STI transmission within this group is great. The attack rate for the 2004 outbreak of HIV in the AFI was 23%, and 61 primary and secondary sexual contacts were exposed in 23 days. A male performer diagnosed as having HIV in 2010 had 16 primary sexual contacts within the 8 weeks before his HIV and oropharyngeal GC diagnosis, 2 of whom were discovered later to have had HIV at the time of filming. In addition to the large number of sexual contacts, the high geographic mobility of performers contributes to the increasing potential for disease transmission. Of the 161 participants with valid zip codes, 20 (12%) designated 7 states other than California as their home of record, and among these, 5 (25%) had an STI (data not shown). If they reside in the states they listed, there is a significant possibility of STIs acquired in LAC being spread to individuals in cities to which performers return.
Also, in most cases, sex work is not a work you can do till retirement, rather opportunities get meager well before reaching middle age. While an ex-prostitute will have an embarrassing-to-explain gap in her “normal” working history, on top of that a former pornographic actress will also be recognizable as such by colleagues and customers. This will far more seriously limit post-sex-work employment opportunities. Your past life as a pornographic actress will always haunt you.
jobermark's idea that the presence of the camera documents abuse, has some plausibility to it, but completely lacks empirical evidence. For example, why do we not know if the allegations against James Deen are true? Why didn't the camera help to either corroborate the accusations against him (or to exonerate him)? Can jobermark show that the porn set is really such a controlled environment? Also, to make his argument cogent, he should have presented some evidence that criminalization of prostitution really reduces, in total, abuse (this is questionable – including for the “Nordic Model”).
To sum it up, there may be many internally consistent ways to legislate pornography production and prostitution (it becomes a question of your values at some point, of course). But regardless what your position on sex work is in general, one thing is beyond reasonable doubt: the current US legislation is grotesque by all measures.
But now to your second question:
I just wanted to see if anyone had any explanation for this.
We can't justify it, but we can easily explain it, if we just free ourselves from the false assumption that legislation in Western countries is generally sane and consistent. It just isn't.
Lawmakers are often ill-informed or irrational. For example, pornography is often framed as a free speech issue. This is a very effective red herring (many posters here fell into that trap): in the contest of inane slogans often dominating political discourse, “porn is protected by the First Amendment!” seems to win against “sex work is paid rape!” …
It's a red herring, because this is not about Marquis de Sade's “Justine, or The Misfortunes of Virtue” or “A Serbian Film” though these works reach the highest levels of depravity. There isn't the slightest problem to say that the production of such works is protected by the First Amendment: the sex is either a result writing down one's imagination (de Sade) or it is simulated (“A Serbian Film”) – but paying someone for real sex would still be illegal. Just because you film and distribute it afterwards it wouldn't magically become legal. Like with any other crime: a violent riot also doesn't become legal when you make a movie about it.
But far worse than the irrationality of lawmakers is that the pressure from lobbyists or just from – there is a fitting German philosophical term – the “Macht des Faktischen” (the normative power of what is current practice) is immense.
Prostitution was de facto banned in all US states except Nevada by the 1920s. In the progressive era, prostitution (like alcohol) was seen as a social ill to be rationally addressed. Pornography only went mainstream in the 1970s, an age of considerable more liberal social mores. And so there just wasn't enough political force then to ban that too.
Today, with the Internet existing, this probably has been cemented. If the US banned pornography production, it would only harm a domestic industry while relocating the issue to another country where demand would increase.