Kotowski, a senior research analyst at Oppenheimer, believes Wells Fargo customers will be more forgiving than the senators and congressmen that have been hammering the bank.
"People will make their decision about where to bank based on convenience," he said. "People hate banks but they love their local bank and their local banker and the people that they deal with all the time at their branch."
One of Stumpf's most vehement critics is Sen. Elizabeth Warren, D-Mass. After Stumpf stepped down Wednesday, she said he should return every nickel he made during the scam and face investigations by the Justice Department and Securities and Exchange Commission.
On Thursday, SEC Chair Mary Jo White told CNBC she is aware of the calls for an investigation but said she does not comment on whether an investigation is underway or whom the agency is investigating.
"We pay a lot of attention across, really, market participants. Obviously Wells Fargo or any other bank as a bank, you have banking regulators as the primary regulators there," she told "Power Lunch."
Kevin Barker, a senior research analyst at Piper Jaffray, believes the scandal will cause some customer turnover.
"I think you are going to see some financial advisors have tough conversations with their clients. I think you are going to see some customers not walk into a branch or chose something else because of the reputation of Wells Fargo," he told "Power Lunch."
He's had an underperform rating on the bank since April, based on fundamentals, not any management issues.
"Their revenue was struggling to grow … and in low interest rate environment, with a lot more regulatory risk, I thought Wells Fargo was going to have difficulty continuing to grow or hit street estimates," Barker said.