Cats are really not that interested in eating the mouse (unless you do not feed them). They are more interested in the hunt and chase. Then the reward when they bring their prize catch to you! Good job kitty!
I think you have a brilliant idea there - maybe you should think of patenting it, with something like Minced Mice Morsels.
My cat certainly eats the mice she catches. I think maybe it depends on cats' early experience - Our cat adopted us when she was about 4-5 months old, and we think she was either a ferral cat, or a kitten that was abandoned because her owner didn't want her. So mice would have been her standard fare. She is certainly not underfed, rather the opposite, so it is not hunger which drives her to eat them.