I understand what you are saying, and I suppose I could call it semantics. But that is not the major issue, if you ask folks about their cholesterol, many will say "My LDL is yadayada..." so it's a common part of the nomenclature.
And if you never ever ate a single food containing cholesterol, your liver would make some for ya!
And in fact you NEED cholesterol, because sitting in the sun converts some of your cholesterol to chole-calciferol, otherwise known as vitamin D3. And the recent findings with vitamin D and cancer are almost as stunning as this one. I think cholesterol plays a role in collagen synthesis too.
Contrary to popular understanding, when we speak of "good and bad" blood cholesterol levels, we are not speaking of different types of cholesterol molecules. Due to their poor solubility in the blood stream, cholesterol, triglycerides and other lipids require transport vehicles such as lipoprotein particles. It is these transport vehicles that determine the "good and bad" nature of cholesterol.