cholesterol is one of the most crucial molecules for survival. It's used to create and maintain cell membranes, and other critical functions. The vast majority is created by the liver, and there are a lot of regulating signals for how much, which is where usually things go off. Low cholesterol production is an extremely serious condition. The "only" problem with high cholesterol is that it builds up inside artery walls, which eventually may or may not dislodge and may or may not cause a heart attack or an embolic stroke. (I'm not a doctor. I just get medication for high cholesterol and have done some research)
> Low cholesterol production is an extremely serious condition.
This is correct, but not in the way you mean it. We know people can effectively produce no LDL cholesterol in their liver and have positive health impacts - these MR studies are a big part of what drove this entire class of cholesterol medications. And the monoclonal antibody versions of PCSK9 inhibitors have shown basically the same results.
Virtually all human cells can produce cholesterol locally de novo, including your brain.