Imagine watching the OT first where we are told Vader took out all the Jedi and we end with Luke as the last one.
In the end, we only see Vader hunting down . . . Children. The other Jedi are pursued by these inquisitors whom Tarkin seems to have no knowledge about in ANH. We also have a Jedi hiding on every block of every planet in the Star Wars galaxy. This effectively means Vader failed in spectacular fashion.