IceBeing - I see your point here, this is a common assumption.
I'm afraid the evidence does suggest that legalising prostitution leads to greater demand and therefore greater numbers of women being exploited and abused: www.catwa.org.au/files/images/Nordic_Model_Pamphlet.pdf
The drugs analogy doesn't really work here. I personally think drugs should be legalised, and not simply because the current laws don't prevent people from taking drugs, but also because there aren't any ethical problems with taking mind altering substances IMO. As long as you don't drive etc., there's no reason why getting high should hurt anyone else. There might be some negative health effects, but then the same is true of alcohol.
Buying sexual access to women's bodies, however, is highly unethical. Even if we made it entirely safe - no STDs, no violence, no rape - there would still be the central act of sex without meaningful consent. Perhaps there are some people in the world who really truly see sex as no big deal, have no emotional attachment to their sexual partners, couldn't give a monkeys whether or not they fancy them, and have nothing invested in their own sexual desires and identities. Maybe these people exist, but I don't think I've ever met one of them. For most people, sex is different from other social interactions and desiring your sexual partner is fundamentally important. This is why rape is such a traumatic act of violation, after all.
And actually plenty of voters do support the legalisation of prostitution, particularly men who like buying sex, which is quite a lot of men! Latest estimates are about 1/8 British men have bought sex at least once (I think! Anyone with better stats please correct me if I'm wrong). Then there are all the people who buy into misogynist ideas about women's bodies being commodities to be bought and sold.
There are plenty of people who see no problem with the idea in theory of selling sex as a form of work, but then ask them if they'd want that for their sister/daughter/mother and they're appalled. We're so used to this idea of a class of invisible women who no one really cares about - prostitutes aren't real people in the minds of many voters.
This twitter exchange between Rachel Moran and Laurie Penny is amazing...
twitter.com/RachelRMoran/status/547580854974025728
This idea that prostitution is alright for some women, just not for me is so offensive. Laurie Penny really gets told here!