Imagine the damage a troop of soldiers with 20-30 of them could have done!
I don't think since they are crew served weapons, And after nine volleys, a bayonet charge would take out the entire unit and capture the puckles, that field use would have been a good idea. However, mounted in a fortress.... you could wreck havoc on folks storming the walls, and would have protection for reloading... shipboard use would be good as well.
During the time period and long after there were rules of war that would have made using the Puckle gun comparable with modern army's using chemical weapons.
Things like that just weren't done.
UM actually as they note a different type of projectile for "Christian" enemies, the gun was very much usable in the warfare of the 18th century. If mounted on ships, you could do whatever you wanted vs. pirates, and the gun was patented the year the Blackbeard died.
The limited use, and the large expense, was probably what caused it's lack of adoption.
The LeMatt revolver is rather cool, but was very expensive and slow to manufacture, and buying a brace of them compared to buying four Colt Navy revolvers and a SxS shotgun, the Colt revolvers win. I submit this is a similar situation as the Puckle.
LD