Here's the thing, for me any way, and I think that a review of old fights and fighters will bear this out.
To do effective body work you don't have to work the body constantly for 5 rounds, exposing yourself to counters etc...Gene Tunney, in his time, was considered a very very effective body puncher because of his straight right to the heart and/or solar plexus and his hook to the body. These days a "good bodypuncher" throws that hook to the side over and over again. But consider the value of a stiff jab to the solar plexus, or the straight right to the heart. The left hook to the heart or solar plexus, the right uppercut to the bottom rib on the right side...These are very effective and relatively safe.
But my point is this. Properly set up and executed one body blow can do the work of round after round of flailing. For perspective. In a streetfight, hands break on heads, that big bone vs. little bone mismatch and very few really experienced fighters- like in the pen, etc..- start off at the head. A quick blow to the chest robs your opponent of breath for the duration of the fight. Once, in my experience, there was a fight in very close quarters and, while one guy won through the use of a "foreign object" the other guy was layed up for nearly three days from two very hard body punches. Pick your shots in others words. Then learn how to punch hard at the opening you have created and one or two body shots can make a tremendous difference in a 3 round fight.