While convenient, it would not be realistic.

IRL the co pilot uses this screen to operate the FLIR unit.
There are of course obvious gameplay reasons for the optics screen (size and positioning). Besides that, the game can't stream high res textures at 30+ fps to make it practical to use this screen as the main targeting device in high load missions.

It doesn't need to stream high res textures at 30+ fps. all it needs is to be a rough visual aid for the pilot, allowing the copilot to increase his situational awareness. It would work just as well to add another to the pilot's side instead of move it away from the copilot (updated ticked with this information). Obviously in real life he would be able to switch between the different pages of the MFCD but in the case of the Hellcat (at least so far), the MFCDs are purely aesthetic and don't actually move, the pilot isn't losing anything by replacing the texture with a camera feed.