If prestigious schools are way beyond your means, then you have to tell your kid what you can afford before they apply. I don’t think it’s a good idea for kids or parents to be saddled with large loans. Especially with people my age, I’ve seen unexpected illness or job loss decimate their savings and plans for working longer.
We saved some money by living in a tiny house for our kids early years. (They shared a bedroom until they were 10.) We buy used cars and drive them for 10 to 15 years. But even then we still didn’t have enough for full tuition. Sadly an inheritence was a big help.