Why would they want the Ludovico to prevent sexual desire?
I get wanting it to have the criminal get sick when he has violent thoughts or when he wants to rape someone, but the idea of eliminating consensual sex as a punishment is kind of extreme (they might have as well have just made eunuchs out of every prisoner).
Also, when the Doctors realized that Alex liked Beethoven and that he would never be able to listen to the 9th again without getting sick, Brodsky said "it can't be helped, this will be the punishment aspect I suppose. The governor should be happy about it." But wouldn't being unable to engage in any kind of sexual contact with a woman be 1000 times more punishing than not being able to hear a song?