>And of course they want to have it both ways. For example, income from illegal prostitution is taxable, but associated expenses can not be claimed as a business expense.
It's complicated and I'm not a lawyer (and certainly not trained in reading court judgements), but this appears to be not true in all cases. Commissioner v. Tellier [1] seems to say that with some well-defined exceptions (although it doesn't appear to go into what those exceptions are), expenses incurred in the development of an illegal business are deductible just like they would be for a legal business. Examples given are paying legal defense fees, and rent and wages paid for a then-illegal gambling operation. So it may well be the case that expenses incurred while developing a career as a prostitute (e.g. phone bills, condoms, advertising, hotel rooms, and travel) could be deductible.
[1]: https://supreme.justia.com/cases/federal/us/383/687/case.htm...
edit: Ah, I read a bit deeper and found the exceptions.
Only where the allowance of a deduction would "frustrate sharply defined national or state policies proscribing particular types of conduct" have we upheld its disallowance [...] Further, the "policies frustrated must be national or state policies evidenced by some governmental declaration of them." [...] Finally, the "test of nondeductibility always is the severity and immediacy of the frustration resulting from allowance of the deduction." [...] In that case, as in Hoover Motor Express Co. v. United States,356 U. S. 38, we upheld the disallowance of deductions claimed by taxpayers for fines and penalties imposed upon them for violating state penal statutes; to allow a deduction in those circumstances would have directly and substantially diluted the actual punishment imposed.
So based on that reading (and again, I'm not a lawyer), it seems like expenses a prostitute incurs would be absolutely deductible, because disallowing them doesn't frustrate the criminalization of the activity.