1. Not every sex worker are doing it for the money only. Many do enjoy doing this. Not every person goes to sex workers for sex but more of a "hired" companionship. 2. Demand for sex would not just disappear. Sex is human nature and sex work has been around since the beginning, it will never "stop". 3. This would increase human trafficking and more abuse to women because of 2 and it has already happened thanks to previous laws like this as mentioned in the article.
This means increased costs for us taxpayers to pay for increased policing due to 3.
You want to make the system cheaper? Decriminalize sex work and/or go after the sex buyers instead.
This would reduce/filter out anyone there for necessity.
What if you paid them not to have sex and they had sex anyways?
What if you paid them not to have sex, but then somebody forced them to anyways?
It's not smart to pay people for something if there is no way to know if you've gotten what you paid for.
How has that worked out for [at least certain types of] religion?