The gist of the pro raw food argument is that since cooked foods
have no enzymes, our (and our pets') bodies have to work harder 
to produce enzymes.  What is never mentioned is that cooking is a 
form of digestion and that it just might be easier on our bodies
to digest cooked food for that reason.  Additionally, the ingesting
body will produce enzymes even when eating raw food.

Like humans, who progressed into cooking their food about 10,000 
years ago, dogs and cats are enjoying progress as well, as 
domesticated entities. 

The "appeal to nature argument" is a narrow view.  It is used to
argue against feeding pets grains and cooked food, not recognizing
the possibility of a symbiotic relationship between animals and 
humans forming as part of evolution.

If one is going to appeal to nature regarding cats and dogs, one
ought to be consistent (and many are) by throwing out cooked food
for humans as well, thereby dispensing with 10,000 years of rich 
culinary cuisine.

I've also heard a claim that raw foods build a stronger immune
system.  I haven't seen the evidence in the form of a study or
anecdotally.  

There are foods which are digested just as easily raw as cooked,
such as fruits and certain vegetables.  I feed them in raw form
for whatever benefit there is, and I do believe there are some
benefits.  The argument can be reframed to include the terms 
"exclusively raw" and "exclusively cooked" or a mix of the two.

With the possible exception of vitamin C, nutritional analysis
of food items varies little between raw and cooked form.  Even the 
b vitamins hold up better than is commonly believed.  Check the USDA 
listings to verify this.  Since vitamin C is obtained exclusively
from fruit, it is not an issue.  There's no digestive benefit in 
cooking fruit.