CEO payments are not _the_ problem. US companies are large, it is a bog company. Most companies in fully private businesses without government payments choose to pay CEO high salaries so that there is a person in charge who spends 24/7 trying to make the company successful.
It is an empirical question which system is better. As mentioned, do we think that public schools are run better than private/charter/etc? Ask people on medicaid and medicare – are these systems better than private insurances (other than possible subsidies).