You can with the appropriate device on certain cars. I retrofit a newer headunit into my older truck and also have the added benefit of turning the backup cam on whenever I want.

http://www.coastaletech.com/index.htm

It would be nice for a lot of reasons but I think over all the net damage from the distraction would be more than the damage saved by people realizing they forgot to pin the trailer coupler and similar stuff. You don't have many reasons to see that field of view at speed since pretty much every reverse camera basically points down.

Rear view mirrors are useful while going forward. But, it's fairly easy to block that line of sight in a full car, thus making the rear view camera a useful backup.