Yes, mouse drinks are alive and well.
http://www.junch.com/wp-content/uploads/2008/10/babymicewinelarge.jpg
It’s a health food (in Asia, many disgusting things are eaten to prolong male erections, i.e. “stamina.”)
I’ve also heard of distilled dog juice (to clean ears) and eaten steamed silkworms (high in protein.)
Another reason we don’t see mice flavored food: Cats don’t buy cat food, people do. People want something tasty for their cats and rodent fricassee doesn’t cut the mustard for most people. However, Sautéed Beef with Gravy would be something most people would buy for their cats.
From my own personal experience with cats, if they chose their own food, moth flavored would be quite popular.
I trained a cat once to eat roaches.
Judging from from the way my two go after the tree frogs which crawl around my windows nearly every night, I think frog might be popular, too.