It's pretty well regulated. Quite close to the degree you're describing but based on fairly comprehensive spot checks rather than regular checks if I'm correct.
The fact that they are so well registered is also one of the reasons why we feature so high on the UN's numbers. In very few other countries can you just survey all registered worker and then label them as trafficking victims whether they agree with that label or not.
Of course there is a risk if you over regulate it that there will still be black market prostitution happening. Especially if those regulations result in a price increase. Which regular health checks and access to social/legal counselling would certainly do.