Should police have the right to pull a driver over with no reason?

They're not supposed to. Even if they pull a random stop, they are limited in the search of the vehicle. Its important to remember not the times that a person was pulled over and something incriminating was found, but all the times a car was searched and nothing was found. That's the whole reason behind the 4th Amendment. It sure is easier for law enforcement to search anywhere and any time they want, but it creates a police state.