It's actually incredibly fortunate for every unemployed person that it's not, in fact, a job whatever misogynists try to pretend. "Sex work" is not a neutral term, it was invented by pimps and those who make money out of people in the sex trade in an attempt to minimise the horrors of what goes on in the industry.
Let us for a moment put aside the reality that you can't unionise if you're a prostitute, that you cannot use PPE and that the entire point of prostitution is to allow men to harm you and that prostitution in no way fits the critera for work (for the most part it is men who use prostitutes which is why I stated it that way).
Let us also put aside the reality that it's not the oldest anything, let alone profession, as that comment was made by a misogynistic fiction writer in 1889, a man well known for being a racist who is normally shunned by the sort of people who quote his fictional comment regularly.
If prostitution WAS actually a job, all unemployed people who have mutual obligations to meet would have to apply for those positions to fulfill their claimant commitments.
There'd be no getting out of it, in order to claim dole money you would have to apply for prostitute jobs if you couldn't get anything else. Because anyone at all can be a prostitute - young, old, disabled, mentally ill - there are vicious, degraded men who would abuse every single type of person imaginable. If it was actually a real job there would be no way of getting out of applying for those positions to meet the wants of abusive men.
Nobody thinks it's work, not really. Misogynists will sometimes pretend otherwise, however. And you're right, there are no middle class parents hoping that Phoebe and Jasper grow up to be prostitutes.
And as the demand for prostitutes always grows with supply, so it would soon become the number one industry in the country, if it was actually proper work with all those unemployed people having to line up for interviews.
So, honestly, thank God it's not an actual job.