Please clarify: You state that the average tuition for a Bachelor's Degree in the US is $110K - $250K. By any chance, do you mean the total cost of attendance at a private US college? I believe you may be mixing apples and oranges.
My daughter is attending a private university. On paper, the yearly cost of attendance at VEU (Very Expensive University) is $65K, falling in the upper range of your quote above. Tuition amounts to $45K. The other $20K is mostly housing, meal plan, travel, and some other optional charges such as supplemental student health insurance. I suppose someone there may actually be paying $65K, but I highly doubt that accounts for many students, as virtually everyone there receives financial assistance of some sort that doesn't have to be repaid (grants, scholarships, work-study, etc.). Expenses not covered by these means are paid out of pocket or financed by loans. With the savings we already have in place, Dear Daughter will graduate without debt.
She considered a state university in our home state, with much lower tuition, housing and fees, which would have actually cost her MORE out of pocket than she is paying at VEU, because she was not offered any significant financial assistance there.
So while I applaud your early research and fully support any student's efforts to graduate without debt, please don't be put off by sticker price tags. If your child is genuinely interested in a particular school, I highly recommend establishing a relationship early on with the recruitment office and learning what kind of financial assistance is available. You may be pleasantly surprised.