A terminal emulator in a GUI environment such as Linux is expected to play nice with the GUI and support mouse-based select, copy and paste, as well as being a terminal emulator, and this means that the terminal itself is consuming mouse events to support text selection.

If you wanted to write a shell that has mouse support you could certainly do so, and this would be based on sending escape codes to the terminal to tell it to return mouse events as input rather than let the terminal consume them itself. The shell could then itself support the clipboard if it wanted to, as well as support mouse editing.

I just googled it, and apparently "fish shell" does exactly this, but your hypothetical user is more likely to stumble upon a bash shell which is letting the terminal emulator consume the mouse events and support copy and paste.