Are you asking if it is a good idea (or required) for the notary or the bank s/he works at to obtain notary insurance against dishonest or negligent actions of the notary?
I know that this type of insurance exists, but I dont know if there is a big demand for the product. We dont have it, in part because dishonest and negligent actions of our notaries rarely arises, but also because we limit what our notaries can do.
For example, 1 of our notaries can notartize a mortgage that our borrowers are giving us, but we wont notarize a signature on a car title, unless the car's owner is also a customer (ie. no notarization for non-customers).