Publicly traded company should pay a small fee to SEC each year and they be responsible to hire auditors, for everyone. Or even better, market bid for auditors with incentives for finding irregularities.
With the current line up of incentives, auditors merely ensures any fraud are slightly better hidden.
SOX is such a well thought of law. It requires any public company listed in thr US to have one auditing company and one "consulting" company supporting the set up internal controls and processes, prepare the books and so on. Those comoanies have to br changed every couple of years (if memory serves well every four years), and you cannot simply switch roles and stay with the same two. Hence a market demand for the big four: A prepares the books, B audits them. Then C replaces A and D replaces B.
Is it? The incentives are not going to be aligned so far as the auditing companies are hired by the company being audited. It doesn't matter how many auditing company there is and the division of labor within.
Think of lobbyists, there are many different flavor of lobbyists, some might even be against the others. They distribute events, campaign finances and other things to legislators and as we know recently even certain members of judiciary. A bad idea in general in terms of the incentives at play.
I’m not saying you shouldn’t hire them (though any local auditor with the same license would likely be better from a quality standpoint), I’m just saying you shouldn’t trust anything they report.