CARLSBAD, Calif. — The debate over big banks' size and complexity is unnecessary in the wake of the Dodd-Frank Act's reforms to the banking system, Wells Fargo Chief Executive John Stumpf said Thursday.

Industry critics are once again questioning whether some banks are "too big to fail," especially after Attorney General Eric Holder said that some are at least too big to prosecute for financial crimes. But Stumpf, the head of the country's fourth-largest bank, rebutted that argument in a speech at a conference on Thursday.

"No company in America, especially financial services, should be too big to fail," he told attendees at American Banker's annual Best Practices in Retail Financial Services Symposium. "In the free enterprise system, success is an outcome that's wonderful, but also failure is another outcome that's necessary."

He added that Dodd-Frank's Title I and Title II, which expand federal oversight of large financial institutions and create an orderly liquidation process, addressed the "too big to fail" question. "I think Dodd-Frank got it right, solved that issue," Stumpf said.

During his speech, which was eventually interrupted by foreclosure protestors, Stumpf addressed other regulatory hot topics for banks, including the Consumer Financial Protection Bureau.

"I support the values that are being espoused by the CFPB — who wouldn't want a level playing field? Who wouldn't want customers to understand what they are buying?" Stumpf said, adding a warning: "For those who think that, 'As long as I disclose it, I have a safe harbor,' those days are over. … The CFPB is not going away."

But he was less sanguine about another regulatory change imposed by the Dodd-Frank Act: the so-called Volcker rule limiting banks' proprietary trading activities.

"Volcker — I worry about that," Stumpf said. "We're in the proprietary business every day. That's called lending."