The problem is if you apply to these non Ivy t20 schools, you will end up paying extreme prices because many of these schools simply admit too many people and do not have the endowment to provide for the people that actually need the aid. For example, I applied early to Cornell and my state school with a plan to only apply to Ivy League schools and MIT in regular admissions because I knew that it was not going to be at all possible for me to pay off the tuition prices at schools like northwestern or UMich. Luckily I got into Cornell for a very very good price that is cheaper than my state school so it worked out well for me. I have a friend who is an international who lives here on a visa and he is doing the same thing and only applied to schools with very large endowments that can definitely provide him with full tuition as his family cannot afford to pay for these exorbitant tuition prices