Means, opportunity and motive are the three crucial elements of investigating a crime and establishing the guilt of its perpetrator. Many crimes cannot be narrowed down by motive until a suspect is on the scene; but acts of terrorism can be. Almost anyone might be responsible for a random killing; but political killings are carried out by those who subscribe to common beliefs.
Eliminate motive from terrorism and it becomes no different than investigating a random killing. If investigators are not allowed to profile potential terrorists based on shared beliefs rooted in violence, that makes it harder to catch terrorists after an act of terror and incredibly difficult before the act of terror takes place.
Investigations consist of connecting the dots. If you can't conceive of a connection, then the investigation is stuck. If you can't make the leap from A to B or add two to two and get four, then you are dependent on lucky breaks. And lucky breaks go both ways. Sometimes investigators get lucky and other times the terrorists get lucky.