It turns out explosions are hot. Lots of explosions in short order will deform or even melt a barrel. If you want lots of explosions quickly you either need some way to cool the barrel (water-cooling the barrel was the standard solution early on) or you need multiple barrels. Spinning those barrels helps cool them a bit, but also lets you stage the action. So while one barrel is being fired the next is being loaded, the previous is having the casing extracted, etc, and each barrel has a longer period in which to cool down before another round gets fired through it.
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