This is a great question. I’ve found myself feeling frustrated when I use GNOME Shell on multiple monitors, and I’ve narrowed it down to this experience: sometimes, when I launch an application on one monitor, I sit there waiting, wondering why the application hasn’t launched, only to eventually realise many seconds later that the application launched and displayed in the other monitor. I’m not sure if this is intended behaviour or not. It would be useful to know what GNOME Shell’s intended behaviour here is.
Here is how I would like it to behave:
The application should launch and display in the same monitor as to where the user launched it.
If the application is already open, then it should be focussed and highlighted. If the application is in the other monitor, then there should be some sort of indication in the monitor where the launch happened to nudge the user towards shifting their gaze to the correct monitor.
Applications should launch quickly, or at least, there should instantaneous feedback that the application is launching or loading.