It's not just Wake, every private school (minus a select few with massive endowments) have priced themselves out of the market for lower middle class families.
The strategy behind tuition pricing is to charge every student the maximum they can "afford" (or the numbers say they can afford) to spend. See http://chronicle.com/blogs/conversation/2012/11/26/the-net-price-myth/ (very good comments to the article, as well.)
IMHO, that is a foolish way to purchase anything. I suppose in theory a family making $150-200K per year could afford full freight at WFU for their kid(s). However, that seems like a foolish waste of money because the family also needs to save for retirement and might have life goals in addition to sending their kid to a country club university.
Wake is no longer a rational choice for upper middle-class families. I don't know enough about the student aid to say whether the price gets low enough to make it a rational choice for lower middle income families. However, Wake would be a rational choice for lower-middle income families if, after discounts, it is priced at or below the cost of UNC.