Because high price is what makes them exclusive and so they compete on high price. Then they give everybody a scholarship - something else they can compete on - which with a little math gives you the real price.

A friend of mine is department head of a local private university. He says that they have consistently found nobody chooses a university for the low price. Meanwhile some choose against a school because if the cost is too low "you must get what you pay for". If you get admitted to that school you automatically get a 40% scholarship - which is to say they don't even want 40% of the money they are charging, but marketing insists they need to charge at least that much. Most students are getting other financial aid above the automatic scholarship as well, only the rich pay the real maximum price. Students who care about costs are looking at what scholarships the school offers them, which is to say everybody knows the sticker price is a lie and they ask about the real costs.

Until people start rejecting the system it won't change. You alone are not enough. So let this be advice to you: don't look at the sticker price. Ask someone to give you a the price after all scholarships apply. It will likely be much more affordable. Though do take your time to understand the fine print, otherwise you could find the scholarship doesn't apply to you after you have the bills and so must take a large loan to pay them.