It would be very difficult to break up the larger firms; they are international in scope and are needed to serve the huge multi-national companies. I wouldn't say it can't be done, but it would be very difficult.
Also, individuals working at the accounting firms do not have a corporate shield, per se. Each is responsible for his or her actions and can be held liable. Each, is, however, shielded from the actions of others within the firm and creditors.
Honesty, I agree, should be a given.
I think we are nearing the point where auditors for individual public companies will be selected by the government (SEC) and rotated every 5 years or so.