First thought was, “WTH? If all those people want is to masturbate using someone else's body, why don't they just pay for a prostitute?”, then I remembered that prostitution is illegal in plenty of places.

Possible reasons:

• Illegality (as you mention).
• Perceived (and as far as I know actual) greater risk of STDs than with their likely alternative partner.
• Price. (ie. "I wish I owned a house" is a plausible wish even if only because then they would not have to rent.)
• Different expected behavior from a sexbot than a prostitute. The "masturbation" experience is presumably enhanced by various behaviors and expression of the sex toy (be it human or robotic). Related to the price reasoning in as much as the price of a "Full Girlfriend Experience" encounter with a prostitute is likely to be far greater than an encounter with someone who puts less effort into acting out an engaged experience.
• Pride, conquest and ego. People like to be achieve and be validated. There are few things that are more validating for humans than to have mates of a suitable level of attractiveness desire your sexual attention.
• Robots are cool. Sexbots are sometimes hilarious.
• Hygene is much easier to manage with sexbots. Not only can you control access to the bot and so prevent exposure to the bodily fluids of unknown strangers, a sexbot can outright detach the relevant robo-parts and wash them in the sink.
• Sexbots can (presumably) be more easily customized to have specific combinations of traits and easily switch between diverse roles or fetishes.