Why should they arrest only the prostitutes and leave their clients alone?

The answer to your question is simply a matter of cost to the city or county to conduct a sting. Often john stings yield little return in value for the cost of conducting the operation. They also are never really effective at curbing prostitution activities.

More prostitutes get busted than johns, part of this is due to the fact that the women become known to police officers because they frequent certain streets where prostitutes are known to walk. Undercover officers (vice) will also drive in and pick a girl up and offer her money for sex. If she accepts, she just broke the law. If she refuses to talk money for sex, he has to let her go. Merely picking up a hooker is not a crime, and it's okay to give a hooker a ride somewhere.

But vice also conducts stings against men (johns). However, this is not as common because again the cost to bust johns is much higher than the cost to bust hookers. It's safer for males officers to pick up hookers and therefore they can operate alone, but it's not nearly as safe for a female undercover officer to get into a john's car (if she even gets in the car). Because johns are often in cars during a pick up, vice has to position more officers and unmarked police cars in the area in case something goes wrong. Additionally, busting prostitutes often leads to information about other illegal activities, such as pimping (a felony as opposed to a misdemeanor for prostitution or hiring a prostitute), sex trafficking, gang activities and drug rings. Comparatively, johns just aren't that interesting.

Like many things in government, it's not a question of morality but a question of cost.

You never heard of a sting operation where a female cop goes undercover posing as a prostitute to arrest the "Johns" (clients)?

Soliciting the services of a prostitute is illegal. In fact, many places will post the mug shot of the "Johns" online for the public to see.

Actually in many states they have cops pose as prostitutes to arrest the clients. Cops are going after both parties because they are both breaking the law.