You literally said "look at most state schools." How can most state schools have a cost that is higher than the average. Also, even your own case proved it. These schools are charging 56k or 34k respectively for 2 semesters. Therefore, a single semester would be 28k or 17k. Far from the 45k you allege in the original post.
Did you misread your own cite? UCLA is $36k for 9 months for in-state students, not $56k. Ohio is $24k for in-state. Anyone looking at these schools out of state is either not paying full price, due to scholarships or other aid, or is not worried about how to pay for it (bank of mom and dad).
Apparently lots of places, since the national average is substantially lower than the Ohio numbers.
But, more importantly, both UCLA and Ohio University are flagship R1s. Likely literally every other public university in Ohio is cheaper than OU, and I'd be unsurprised if UCLA is one of the more expensive public options in CA (wouldn't know, never lived in CA).
e: sure enough, the total cost at Youngstown State is 22K (tuition 10K, the rest is food and housing).
As an aside, including room and board in college prices always struck me as a bit odd (except in cases where living in a dorm is required, I guess, but that's somewhat rare). Do non-college-students not eat/drink/sleep?
Colleges/Universities and expensive enough and screwed up enough that exaggeration isn't necessary.
https://admission.ucla.edu/tuition-aid/tuition-fees 56k 9 months.
https://www.ohio.edu/financial-aid/cost
34k 9 months
9 months is considered 2 semesters.
per semester.
wouldn't consider ohio personally though. but beats your average by a good 30%. Not sure where it can get cheaper than Ohio.