Given what occurred in WW1 and the British tactics evolving to the convoy system and their advice to the US for its use, I find it difficult to understand the delay in using it.
According to the History of World War 2, by E. Bauer, Admiral King had a staunch anti-British attitude in all things, which would include British naval tactics. The book doesn't delve into the reasons why King felt this way. The same book also reveals that at the beginning of the war, the doctrine for both sides at the time believed eliminating direct military units was more effective than disrupting supply lines. The U-boat commander, Admiral Karl Dönitz, obviously did not believe this doctrine since he commanded the U-boats to go after shipping almost immediately. But this attitude along with the doctrine led King to take few effective actions early in the war. He instead pursued a policy of aggressive anti-submarine actions. The tonnage of ships sank worried Churchill so much that eventually he wrote letters to Roosevelt and the worries in the letters trickled down to King, who started taking action around 1942. Apparently, at the height of the U-boat successes, an average of 700,000 tonnes of shipping was sunk for a few months.
On a side note, we can point to another reason why if WW2 had to have someone running strategy, it was great that Hitler was doing it. From the book again, pre-war servicing crews were redirected away from making subs operational and during the war a few operational subs were redirected uselessly elsewhere (Norway and the Mediterranean). Both were due to Hitler's insistence. Dönitz only had half of the existing subs to use at the start of the war. Imagine how much worse it could have been for Britain.