Wasn't Generals the one where the AI, at least on hard, got supply bonuses every so often? They do need resources and killing their supply depots and secondary sources (drop pad, hackers, etc) will hurt them, but it will never completely stop them, since they will basically get a supply drop once in a while.
One of my favorite memories of ZH was using Air Force and killing a particularly difficultd enemy's command center with my general's powers and a massed airstrike, while simultaneously using Auroras to kill each and every one of his dozers. No way to build dozers, and no way to build a command center to build more dozers. From there on, I took great pleasure in picking apart his base, knowing that each reactor I killed, even if it cost 3 auroras, was gone for good.