Ah, the Anglo-Zanzibar war. Again, I would manintain, you have to look at the size of the ground forces too.
The late sultan of Zanzibar had been allowed by the British to have a maximum army of 1000 men, and most of them were not in the capital at any time anyway. Before the confrontation, the new sultan only had 700 soldiers, and some 2000 or so civilians who had taken up arms.
Meanwhile, by the 25'th, the British had gathered a ground force of slightly over 1000, standing ready to storm the palace. Actual soldiers. On the 26'th further marines and sailors were brought by ship.
That's not counting the fact that the majority of the town's population was favouring the British, so if push came to shove, the civilians that had sided with the sultan were a minority.
At this point the British could already win on the ground, although attacking a fortified position like the palace would have caused severe losses.
Then came the artillery pissing contest. The British artillery barrage wasn't just a show of power, but it took out pretty much all of the sultan's artillery, and killed 500 of his troops, which pretty much means about 20% of all the army he had. At this point, no doubt the rest were having a MAJOR morale problem (losing 20% of your mates in half a hour will shake any army, but doubly so some civilians who took dad's old rifle), and between that and the loss of their own artillery, the balance of power at this point heavily favoured the British ground forces.
So basically I put forward to you the idea that again, it was the actual presence of boots on the ground that won the war. While one can correctly say that they didn't ACTUALLY have to do an assault, they were there, it was clear that the assault would come next, and it was clear that they would win it.
It wasn't JUST the artillery barrage that won the war.