Definitely, but with a lot of safeguards in place.
First of all, think of all the revenue the government can get from a billion-dollar industry. The U.S. is in economic strife; they don't have the place to be cocky about where their money comes from. Besides, how is it immoral to pay for sex? It's the person's body, and they can decide how to use it, providing they're not putting others in danger. Plenty of people use sex as a device to get what they want from others, and nobody complains nearly as much. It's nothing new to use sex to make some kind of profit. Everybody knows what else escort services really implement, but their businesses get taxed. It would be nothing new.
Secondly... there will be less of them that get killed or beaten- covertness is understandable for some clients, but it also opens a gaping hole for those of vile intentions to abuse and harm them. With appropriate safeguards in place, there would be much less risks of them getting harmed. Should it become legal, organisations that make use of prostitutes should be legally obligated to fund for sexual health tests to "keep them clean," you could say, as well as healthy. Clients should be forced to sign logs of some kind, so that if they assault a prostitute, it would be much easier to track them down. Of course, the documents, like client records, would be treated with the utmost confidence.
Unregistered prostitution should be illegal, as it can be very unsafe for both parties. Not only that, but by applying procedural enrolment, authorities can be sure that the person seeking to become a hooker was not coerced and is free from sexually transmitted disease. Of course, the former can't be 100% absolute, but it's a start. No, this won't make people less likely to become prostitutes- people that choose this path will choose it anyway.
Also, think of the decrease in rapes if prostitution becomes more readily and legally available. One can see a hooker without fear of getting arrested or publicly shamed.
"It is estimated that if prostitution were legalized in the United States, the rape rate would decrease by roughly 25% for a decrease of approximately 25,000 rapes per year... ...[T]he analysis seems to support the hypothesis that the rape rate could be lowered if prostitution was more readily available. This would be accomplished in most countries by its legalization."
- Kirby R. Cundiff, PhD, Associate Professor of Finance at Northeastern State University
As opposed to (granted, this is an Australian statistic, but the principle remains the same):
"A study conducted in Queensland... show[ed] a 149% increase in the rate of rape when legal brothels were closed in 1959."
- Linda M. Rio Reichmann, JD, Director of the American Bar Association's (ABA) Child Custody Pro Bono Project