ADA organization is a bit different, the battalions have their own Stinger platoon so attachments from the ADA Battalion is more of a Brigade-level sort of thing. The only time that I have ever heard of or witnessed an ADA attachment to a line battalion was when the battalion was conducting a solo operation such as rear guard or advanced guard, even then, it was normally no more than a gun section of two Vulcan tracks, the Chaparrals almost always cover the rear areas.
Engineers tasked on an as needed basis, usually on a platoon tasked to a company sort of thing...although...for Desert Storm, the attachment was a full engineer company to a battalion.
The battalions also field their own Scout platoons, so the Divisional Cavalry Squadron is seldom broken down and attached.
During the 1980s, a lot of experiments were run with the Cav's troops being reinforced by an attached tank platoon. Because the Cav was not used to cross-attachment (and even more important, the line dawgs were not used to the recon role), this led to the HMMWV/TOW augementation and later the permanent attachment of a tank platoon to each of the two ground troops.
Another set of units that do not cross-attach are the Combat Aviation Battalions, they are more like the artillery, with a company of attack helicopters tasked to support a specific battalion.
Generally, the further back the unit, the less likely it will cross-attach.
I was looking through some old manuals I have, and for the 1980s timeframe, the Marines would attach support units to the regiment/battalion with the local commander attaching the support to specific units. The overall impression I get is that the Marines do not cross-attach to the degree that the Army does.
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The reason that the American Army does so well in wartime, is that war is chaos, and the American Army practices chaos on a daily basis.
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