I have BOA & WF but have never had issues within the US unless I'm logging in from a new computer in which case I'm asked a security question/given a code (Chase ?). I don't remember if I tried to use them abroad. One nuisance with WF are the extra ATM fees when using it abroad. My main bank is a small local brick & mortar bank that refunds ATM fees with certain conditions.

Some banks will send the security code only to a cell. The workaround is to set up a Google Voice number and have your GV forward to another non-Gmail email account. Then you have the option of logging into two email accounts to get your code.