Airlines profited around $28 billion in 2019 [1].
If they were publicly owned, the prices of flights would just go down until there was no profit. Also, the CEOs wouldn't be paid tens of millions of dollars per year [2], so again, prices would go down.
[1] https://www.cnbc.com/2019/06/02/airline-industry-cuts-profit...
[2] https://skift.com/2019/05/29/united-wont-pay-munoz-a-full-bo...