When I lived in Wyoming and could get lots of doe/fawn tags for $5 each, several times I intentionally shot fawns (deer and antelope).  For the same reason I occasionally will pay $12 for a nice 10 oz beef tenderloin steak, instead of buying 4 lbs of chuck with the same money.  Slow cooking the entire round muscles and backstraps on a grill, not much meat but quality to die for.  If it was my only tag, like generally is the case here, I probably wouldn't shoot a fawn except for the last minutes of the season.  
I would still happily shoot an elk calf.  The last one I shot, I thought there were an adult cow, a yearling and a calf - I shot the "yearling", turned out it was a big calf.  76lbs of absolutely orgasmic eats.