> But keeping buying sex illegal means they will choose to buy sex in areas where they feel safe from the law. This will make people who have no choice but to sell sex operate in a less safe environment.
This statement has the same fallacy that the following statement does: "Keeping child labor illegal means children will choose to work in places where they feel less safe from the law. This will make young children who feel they have no choice but to work in a factory operate in a less safe environment."
The very fact that a certain choice is legal increases the economic incentives to pressure people into making that choice; in contrast, removing a choice by making it illegal incentivizes employers to offer alternate choices that are potentially less exploitative. When child labor is illegal, employers are incentivized to pay their workers a high enough wage to support the whole family without children having to work. When the option of child labor is taken off the table, workers end up in a better negotiating position.
The same is true of prostitution. When people can make money legally off of prostitution, they will be incentivized to go into the prostitution business and hire prostitutes. When they can't do that, they will be incentivized to go into a different line of work, and create employment opportunities for women that are less inherently exploitative.