Legalization of prostitution is a problem by itself, because the regulatory costs end up being borne by the sex workers (more on that in a tic). For prostitutes that are working at a subsistence level or only doing sex work occasionally as a stop-gap–which is the majority of voluntary prostitution–that’s not going to work. And what do you do, for instance, when a registered sex worker suddenly tests positive for HIV, or hepatitis C? Revoke their license, and then…? Legalizing doesn’t eliminate trafficking, it just pushes the prices for trafficked prostitutes down, because trafficked prostitutes are slaves.
There are definitely harm-reduction models that can, and do, work for sex work, but legalization and regulation–when that regulatory costs are paid by either the sex worker or the customer–will not work the way you think for harm reduction. For the system to work as intended, you would also need things like national single-payer healthcare (…that isn’t constantly getting funding slashed by conservatives), and licensing that was both on-demand and free to the licensee, and you would need something to deal with the loss of income if they contracted an incurable STI. (Otherwise they would continue working, which would be a public health risk.) Inspections, compliance measures, et al. could not be a cost borne by the sew worker/clients or else you’d see non-compliance with regulatory measures. Most sex-worker advocates call for decriminalization rather than legalization/regulation because that’s the model that moves the most risk away from the sex worker, but you do need to also balance the needs of the worker against the the needs of society to a degree.