I agree that the experiment was groundbreaking. Most people seem to accept the "primordial soup" argument without question. However, I do also think that there is no way to actually recreate the conditions that existed when life was created.
Stanley Miller and Howard Urey's famous experiment was groundbreaking, because prior researchers had simply accepted that idea that the origin of life would only be theoretical, and that there was no way to pursue actual scientific research on it. The Miller-Urey experiment was the first attempt to replicate the processes of early Earth in the lab.
Some of Miller's original premises have been questioned - for instance, some believe that the atmospheric composition of his experiment may not truly be representative of early Earth conditions. However the concept itself still stands, and the experiment pointed the way for generations of researchers looking at life's origins both on Earth and, potentially, elsewhere in space.