I think its been a tradition and pattern of the various tv shows and movies pushing Alfred's role bigger and bigger.
On top of the serial and the 60s show examples listed, Michael Gough in the movies had a very strong role in Batman's crime fighting. In Batman Returns he was monitoring the Penguins attack from the cave for Batman. The Animated Series I believe was the first to introduce that he had a military, British secret agent background. Which was used more prominently in the Nolan films
I had not read the actual comics much in years but he is still basically just the butler. Probably because there is this whole army of ex Robins, his role is not as important.