Your post is partly right in that there was less dependency on CA as a branch. But you are ignoring the main reason that created the many AAA battalions.
When Antiaircraft Artillery was created during WWI, it was assigned to the Coast Artillery. Both branches defended US from attacks beyond its borders and both tried to place their shot on target. Whenever there was a CA harbor defense regiment active, they took care of all guns in the installation, be they AA or a big gun. But at the same time, purely antiaircraft artillery regiments were created assigned to the Coast Artillery. For example, 60th Coast Artillery (Anti Aircraft) served in the Philippines. 72nd Coast Artillery (AA) served in Panama. These soldiers had the letters CAC on their DD214 forms. Meaning Coast Artillery Corps.
The Coast Artillery (AA) regiment in 1936 had one battalion of 3-inch guns (1st Battalion), one battalion of machine guns (2nd Battalion), and one battery of searchlights. This battery in 1942 was expanded into a battalion (3rd Battalion). Late '42 it was found that the antiaircraft artillery missions resulted in problems for the regiments. The regimental structure was too rigid, and in 1943 all CA (AA) regiments were inactivated, with their 1st Battalions became AAA Gun Battalions. The 2nd Battalions became the AAA Auto Weapons Battalions. The 3rd Battalions became the AAA Searchlight Battalions.
Unit histories are available from the National Records and Archives Administration. I suggest they write to the one at College Park, Maryland. They can tell whether they have the actual history.
National Archives at College Park 8601 Adelphi Road College Park, MD 20740-6001
That is how I have a copy of the history of the 762nd AAA Gun Battalion, formerly 1st Battalion, 72nd CA (AA); and of the 891st AAA Gun Battalion, formerly 1st Battalion, 615th CA (AA).
There were a lot of AA battalions activated in 1943, later some of these were deactivated along with Coast Artillery (Harbor Defense) regiments because in 1944 it was decided that more men were needed in Europe...