Convenient for the sake of Drama ***Warning spoiler alert***
They had to make the bad guys so dumb that they thought that they could escape in Becks car without being apprehended.
That is the only way that they could show Beck so ashamed that he didn't want to throw them in jail. Without that insanely stupid behavior there is no way that Beck would have had to be confronted with his Trauma. He could very easily have denied it ever took place or "forgot" all about it on purpose.
Without that very unlikely and stupid behavior by the perpetrators he wouldn't need to be confronted or have to explain anything to his colleagues either.
Sure there was a witness but if Beck himself wasn't keen to help he could have given fake descriptions of them or said he didn't remember. As it turned out, they were apprehended in his car and VERY likely to be the perpetrators. Beck had conveniently no way out. In real life he could have decided to walk away for good.