Yes in the USA entrapment is illegal and cannot legally be done by normal cops.
Only Government Agents Can legally Entrap someone into committing a crime.
The Entrapment law is a leash intended to curb outrageous conduct by police officers and other public officials.
An entrapment defense does not arise if private individuals convince defendants to commit crimes.
In legal terms Entrapment is a practice in which a law enforcement agent or agent of the state induces a person to commit a "crime" that the person would have otherwise been unlikely or unwilling to commit.
In some ways this entrapment is wrong and other times it does need to be done to get criminals and thieves off the street.
But sometimes entrapment is done for less serious crimes and then in those cases it does not make sense for them to do it.