Yes, provided it is controlled.
I can't pretend that I would be okay with seeing a relative live out his or her life as a prostitute (there are plenty of male prostitutes, it's not just confined to women), but I also cannot pretend that I have the authority to tell them what they can do with their body.
Some people make the decision to go into prostitution. I don't know why they make that decision. But some do, of their own free will. Prostitution has been around since the dawn of the human species, it exists in every nation across the globe. No country has actually successfully managed to ban it - even puritancial Saudi Arabia and Pakistan have their fair share of brothels (and alcohol!). Like Alcohol you can't legislate it away.
If we continue to drive sex-workers underground, things get nasty. Without regulations and government oversight, prostitution becomes a much more dangerous, exploitative business. Bringing it above ground allows us to ensure that sex-workers are properly treated and well paid and that they aren't forced into the business. If we continue to arrest prostitutes and treat them as criminals, we leave them vulnerable to the really nasty elements of the underground.
In Brisbane, we have legalized prostitution. It's often dressed up as "escort" services and whatnot, but if you've seen the advertisements they put out, it's not really an "escort" service. The legalization of prostituion has NOT caused everyone to strip off their clothes and have orgies in the street. Rather, what it has done, has been to get Prostitutes of the dangerous dark streets and into well known, policed business areas and buildings. We don't see prostitues on the streets anymore (or at least, I haven't seen any, but then again, I don't really know what a prostitute dresses like, so I don't know if they are there or not. They could be still there, but anyway you get my point). This allows for sex workers who want to be in the job to work openly, and it allows the police to REALLY focus their attention on illegal forced sexual servitude, which is still a huge problem around the world.
So legalizing prostitution would:
1) Make life safer for those who choose to go into the sex-business
2) Allow the police to tackle the real problems of forced prostitution
3) Ensure that sex-workers are fairly paid.
Nothing comes for demonizing prostitutes or arresting them or driving them underground. Again, Saudi Arabia and Pakistan often KILL prostitutes, yet brothels still thrive underground in those countries (so do bars for that matter - I won't forget the time I saw a wealthly Saudi Business man crack open a few cold ones, right in front of me in the hotel!).
Prostitutes are human beings. I might not understand WHY they went into that business. You might not understand. But that doesn't mean they have no rights or that the deserve to have their lives ruined. They need to eat food like everyone else, and that's just the way that they choose to do it. It's not the safest job, it's definitely not the most well paying job and it's doesn't give much dignity, but it's the job they are in. The LAST thing they need is to be worried about going to jail if they go to the police.
If you can't get rid of it, you've got to plan for it.