Because Gosho wants the mystery to unfold a certain way in order to be interesting; he is using different witness testimonies from the past one after another that the reader must untangle to uncover Rum's true form. Coincidental cases involving the past are the easiest way to approach the subject although it sacrifices some realism to have Conan run into one relevant case after the other.
/Doylist answer
Haneda Shuukichi's recent Shougi victories, especially his recent claim of all seven titles which made popular news, have suddenly forced people to recall the late Haneda Kohji. People involved in Kohji's death are thus prompted to act on their memories since it is on the forefront of their minds.
/Watsonian answer