I think you misunderstood what I was trying to say. I was referring to counter battery fire or troops sufficiently close to snipe at cannoneers. In those cases you need to fire as rapidly as you can while still hitting the targets. Having a full caisson with your piece put out of action doesn't do any good either.

If a piece is not dueling, then yes, I would expect it to maintain a measured pace. The Gettysburg bombardment is a useful illustration. Hunt ordered his arty not to fire (though he was overridden in the case of some batteries.) By not firing they did indeed conserve long range ammo for the expected infantry attack. They also kept their positions more hidden and prevented the CSA gunners from focusing fire on them. (The few who returned fire were torn to shreds.) Hunt saw the proper role as repelling the charge, not dueling with enemy artillery.

Contrast this with the CSA gunners who appear to have expended their ammo in about the time frame one would expect for spirited firing with 3-4 chests of ammo per gun. This makes sense though because the CSA were on the offensive and were forbidden to fire over their troops. Their best chance was to try to knockout any enemy guns rapidly then continue the bombardment until nearly out of ammo. Unfortunately, the supply wagons had been moved away so they couldn't replenish either. Not that they could have done much in support other than firing on enfilading batteries to either side of their own columns.