Why can’t you copy and paste files in FTP software?

This is something always bothered me, and a simple search on Google shows millions of results on the subject, so it seems to be a real issue: why can't you do simple file operations such as copy+paste inside FTP software (like Filezilla, CuteFTP, SmartFTP and the likes)?

I know you can use ssh, and most hosting services have some kind of file manager that allows to do this on a GUI, so it seems it only affects FTP. Furthermore, the fact that hosts offer this GUI would neglect security reasons.

So, why is this not possible? Technical reasons? Protocol issues? Security concerns (don't think so, but still)? It obviously is very annoying to any user and provides a very poor experience, so I'm wondering what is the cause of this, and what prevents this from being fixed