It's not. There are plenty (female) hard-core 2nd-wave feminists that are all for legalization of prostitution, citing self-empowerment, economic empowerment and the acceptance of female sexuality.
You say -- to paraphrase -- 'the True Feminist only speaks what's good for women and only I decide what's good for women'. That's not an argument, it's a dogma.
This is not particular to feminism. If we can clearly see someone choosing a self destructive lifestyle (i.e. drugs), even if it is what they really want, our responsibility is to help them get out of it.
Prohibition itself has never stopped anyone from doing anything stupid. All it ever does is empower scrupulous people to make money of it.
If you argue for changing the economic setup so that nobody has to do work they would rather not be doing -- I'm all for it. But don't make it sound as if prostitution was anything special in that regard.
And yes that same argument, our body is important to us, I'll repeat (for the last time) is important to all performance artists. Let's not project "I would be offended by this use of my body" to everyone in the world.
Prostitution destroys society. It breaks up families. It leads to fatherless children. It spreads STDs. It teaches men to treat women as sex objects. It denigrates sex in general to pleasure instead of its main purpose of creating the next generation.
Prostitution (might) spread STDs because there is no regulation and oversight, no health-check mandate for prostitutes (of either gender).
All those issues you cite don't really stem from prostitution and making/keeping prostitution illegal will not make them go away.
Even regulated, the number of STD exposures climbs exponentially with prostitution. That is just the unavoidable math of having massive numbers of sex partners.
Seriously; prostitution is a symptom, not the cause.
With regards to diseases; diseases spread with any physical contact between humans. I still don't think that it would be a good thing to stop having contact.
Making prostitution illegal will not make it go away. It has been with us for before we climbed out of the trees, it will be with us long after we've stopped reading words. Making it illegal will just rob the prostitutes of potential protection and safety.