They build up in the artery walls to plug lesions. It's a healing process. The problem isn't the this response, the problem is the lesions that require it. Those are a symptom of chronic inflammation, not excess cholesterol. You don't get plaques just because you have a lot of extra cholesterol floating around.
"I am trying to stay off of statins, but my cholesterol is sky high, regardless of significant dietary and lifestyle changes."
I know nothing about your circumstances, but I'll point out that some people have abnormally high cholesterol. It's called hypercholesterolemia. It is not necessarily a danger, since again, heart disease is not a function of elevated cholesterol.