> Well, the body has a whole mechanism for manufacturing cholesterol, so it must be good for something. It seems obvious that there's some level at which low cholesterol must cause death.

Agreed.

> A U-shaped cholesterol-mortality curve is pretty much guaranteed to exist.

Yes, this is a necessary consequence of the first observation. Mortality will go to 100% if cholesterol is too low or too high.

> The only question is where the minimum is.

But I don't think this is right. You can calculate a mortality-by-cholesterol-level curve for the population, and it will have a minimum somewhere. But it doesn't follow that it would be good for you, even in a sense restricted to all-cause mortality, if you moved your personal cholesterol level closer to the minimum value on that curve. Most people in the population aren't like you.