So, let me guess: they can establish a connection to the Internet, then run a browser to access the online banking web site, yes?? Would that be a "dial-up" connection or is it "broadband"?? What are the transmission speeds for public Wi-Fi networks??

My bank, at least, will still use the IP address assigned to the connection by the ISP to determine whether their web site "recognizes" a computer. Which is really not a good idea when the IP address is "dynamic" and not "static".

I do not know whether every smartphone has a unique Machine Address (MAC address). IIRC, the MAC address of the computer (device) that sends a TCP/IP packet is in the packet header. That is what the LAN router uses to decide which computer is the destination for an incoming packet. (Or so I have heard, I am not an expert on this matter.)