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If the shaft was open with an intact casing and the casing was concave. Eight sided pyramid and all.
We'd have a huge catchment area and sides that would direct the water flow toward the centre line of the casing.

Exactly. It could explain the concave casing, the eight sided pyramid: It's possible that it was built this way to catch water, I always believed this.
But if this is true, I don't think the pyramidbuilders were trying to catch water from torrential rain once every 20 years. There must have been a lot more rain at the time when the pyramid was built. This could be evidence that it was built during the period of monsoon rains, 8,500 BC.