Alzheimer's is clearly correlated with a deficiency in the supply of fat and cholesterol to the brain. IDL, when functioning properly, is actually incredibly efficient in cholesterol and fat throughput from the blood across cell membranes, compared to LDL . It gives up its contents much more readily than the other apo's. And it achieves this as a direct consequence of apoE. IDL (as well as LDL) in the blood delivers fats and cholesterol to the astrocytes in the brain, and the astrocytes can thus use this external source instead of having to produce these nutrients themselves. I suspect, in fact, that astrocytes only produce a private supply when the external supply is insufficient, and they do so reluctantly.
Why would it be disadvantageous for an astrocyte to synthesize its own fats and cholesterol? In my opinion, the answer has to do with oxygen. An astrocyte needs a significant energy source to synthesize fats and cholesterol, and this energy is usually supplied by glucose from the blood stream. Furthermore, the end-product of glucose metabolism is acetyl-Coenzyme A, the precursor to both fatty acids and cholesterol. Glucose can be consumed very efficiently in the mitochondria, internal structures within the cell cytoplasm, via aerobic processes that require oxygen. The glucose is broken down to produce acetyl-Coenzyme A as an end-product, as well as ATP, the source of energy in all cells.
However, oxygen is toxic to lipids (fats), because it oxidizes them and makes them rancid. Lipids are fragile if not encased in a protective shell like IDL, HDL, or LDL. Once they are rancid they are susceptible to infection by invasive agents like bacteria and viruses. So an astrocyte trying to synthesize a lipid has to be very careful to keep oxygen out, yet oxygen is needed for efficient metabolism of glucose, which will provide both the fuel (ATP) and the raw materials (acetyl-Coenzyme A) for fat and cholesterol synthesis.
What to do? Well, it turns out that there is an alternative, although much less efficient, solution: to metabolize glucose anaerobically directly in the cytoplasm. This process does not depend on oxygen (a great advantage) but it also yields substantially less ATP (only 6 ATP as contrasted with 30 if glucose is metabolized aerobically in the mitochondria). The end product of this anaerobic step is a substance called pyruvate, which could be further broken down to yield a lot more energy, but this process is not accessible to all cells, and it turns out that the astrocytes need help for this to happen, which is where amyloid-beta comes in.