Is that more common than HTTPS, simpler, and a standard feature of FTP? I daresay not. In other words, you're making up a convoluted scenario and pretending it's still plain FTP, even though your toolchain got far more esoteric.
It's esoteric because proper key management is a fulltime job at best.
And every attempt at doing key management better is met with hostility from many in the community (rightfully or otherwise) as they tend to sacrifice "absolute security" in the name of greater "usable security" (often by centralizing the trust system in some way).
At least in Canada the last bank integration I worked on was FTPS (FTP over SSL). Files were otherwise in plaintext with account numbers and everything.
There were a few blog posts posted here from a payroll company not too far back. They explicitly kept using the term “SFTP” so I have some hope that at least a good portion of banks aren’t completely broken.