We're not accepting uncritically that universities are private endeavors. We're accepting that some are and they should be allowed to continue to exist.
UNC Chapel Hill (what I assume you mean by North Carolina) costs students from the state $8,834 USD. Out-of-state tuition is $33,916. I would not call either number "shockingly expensive."
Michigan is $14,402 and $45,410. UVA is similar. Quite a bit more but still not anything shocking. Minnesota is similar but out-of-state tuition is just $23k.
[Edited to add: Some people have more than one child. Some of them have more than one child in college at the same time.]
I still don't consider it shockingly expensive - it's been the top value public university in the country for 18 years in a row.
https://www.newsobserver.com/news/local/article233110061.htm...
No wonder university is a privilege of the wealthy.
Let's assume that the average high school graduate is an outlier, some financial wizard or an uneducated but driven high-earner with the wisdom and ability to save an entire years' base income for a college fund before they're out the high school's door, giving them just around enough to pay for four years of tuition at a cheaper public university.
So let's assume they have some kind of neat free housing deal where they work the dorm cafeteria and get their meals free as well.
They would then also have to be one of the 33% of undergrads who actually complete a degree in 4 years in public universities to wrap this miracle up without debt.
This person doesn't exist. And yet, achieving a debt-free college education at a reasonable age has been possible in previous decades and continues to be possible in other nations.