Personal Banking Dept. is wanting to offer a checking product whereby the consumer receives both a paper statement AND their statements electronically within the mobile banking portal. Later, they will contact the customer and ask them if they want to receive just the paper statements and will have the customer go thru the e-sign process to cease the paper version. Does anyone see a problem with this process? appreciate your thoughts.

As long as the "e-sign process" includes providing the information the bank is required to provide to the consumer about how the electronic delivery will take place, whether (and at what cost) paper copies will be available, the hardware and software requirements, etc., and the consumer consents in a matter that demonstrates his/her ability to access an electronic records in the prescribed manner, you should be fine. One you have the demonstrable consent, you can stop sending the paper statement.

I agree with John but will add that I've some banks get in trouble because they provide paper and e-statements. They rely on the paper for compliance and that is fine. Then as a cost cutting measure they revert to e-statements and haven't done the E-SIGN 101(c) (7001(c) in the version linked below) hoops with consumers (commercial accounts are easier and don't require all this) or haven't updated the agreement to what is the current offering.

https://www.bankersonline.com/regulations/esign-7001

Be careful to time the discontinuation of paper to occur only after you have the depositor's consent.