Interesting, but I would personally like to leave the government out of this (let's not introduce deeper/political conflicts of interests).

What about just standardizing the fees charged for audits and doing a fixed rotation (rotate e.g. once every 4 years) of assignments of auditing companies to clients (companies being audited)?

This way on one hand the conflict of interest by paying megabucks to auditing firms (to get a positive audit outcome) would vanish (as the fees would be fixed), on the other hand a auditing companies would lose the tendency to try to stick to a particular client (by providing positive audit outcome).