1. not all providers tell the truth
2. some cops are real fuckers
3. in some jurisdiction, cops can use their dicktions, but it is usually not correct behavior
4. you are confusing entrapment with arrest for a violation, this is not entrapment. This is simply fucking, cops like to do it as much as everyone else.
5.If the girl was not paid then she has a civil action in contract but I doubt she would win.
6. In simple words, entrapment is when you induce a person to commit a crime he/she would not have committed without your inducement.

A cop engaging is sexual intercourse with a prostitute is very risky and not really necessary for the arrest to occur.  I'd be willing to bet that your provider is not telling you the story the way it actually happened.

You have to prove that absent any actions of LE, you would not have been engaging in any illegal activity.

Since we clients and providers are actively trying to hook up with one another, this defense will rarely work.

You'd have to prove that LE almost literally yanked you off the street and made you pay for sex to get any traction there.

(still not a lawyer)

Didn't I see this on Law&Order... yeah, the hooker immediately claimed she was raped and demanded to be taken to the hospital for a rape kit.  They found semen and they matched it to the cop.  That put the cop in the position of either saying he raped her or that he paid her money for sex.  The case got tossed since the DA couldn't put the cop on the stand... then it turned out that the cop was a serial rapist... yeah, I remember it.