The board chooses the CEO and his salary; if the board wants to give some of the salary in the form of jet reimbursements it's not really any concern beyond them and the shareholders.
It is a concern for the tax payers if company is paying it as expense and deducting it from taxes instead of paying it as (taxed) salary and him doing what he wants with his money. Don't you have rules what can be expensed in the US?
And personal use is accounted for (if paid by the company) and remanded as salary/perks.
I even got affected by that at a restaurant I worked at; they fed us and we got a small "virtual" payment that would show up on our taxes for that meal.
My recollection (I’m not checking) is that congress passed a law restricting the deductibility of private air flights, but that there’s widespread fraud in the form of “security consultants” advising boards that such flights are necessary for security purposes and so they are deducted anyway.
It’s pretty unreal when you think about it that our culture has not small cadres of credentialed, professional liars for hire. Not just for CEOs either, think about the fake service pets for another example.