Blown caps are common because they get overvolted or they wear out. Why would the first N capacitors fail when they're all splitting the voltage? (Assuming the string of caps is properly isolated from the outside world. Is parasitic capacitance unavoidably high?)

I presume that if you model a lightning pulse and treat the leading edge as a step function (ignoring leaders etc), then a tiny amount of inductance inside the capacitor will cause the voltage to transiently exceed the rating. Since the capacitors all start at 0 Volts, then the one connected to the lightening will fail explosively. I would expect all of them to fail like dominos since plasma is a good conductor and each failure would not significantly soften the rise-time.

Perhaps inductance is the answer? Connect your lightning rod to a beefy primary of a transformer, with lots of tiny secondaries; each sourcing a capacitor.

The primary would be a rod (zero turns). Or probably better a large circle of ribbons (current travels down surface of the circle because electrons repel each other). With independent current transformers around each ribbon.

I had also wondered about a multi-strand design with different lengths as a way to smear the initial step.

The real issue is that a strike is fast transient currents: I suspect that my normal calculations for voltage, current, transformers, inductance and capacitance don't hold. The amount of charge that travels through a lightning bolt is typically around 15 C, although for large bolts this can be up to 350 C.

The main problem with the whole idea is that the actual amount of kW is not that large. "a lightning bolt, which has over five billion Joules of energy, which could provide one household with all their energy needs for a month" which I presume is assuming 100% conversion and storage efficiency...

Edit: and this really screws with any possible design: "Occasionally a lightning stroke will travel from the positive charge region in the top of the thunderstorm cloud to ground. This type of lightning is called positive lightning and accounts for about 5% of all cloud-to-ground lightning strikes. Positive lightning is powerful and typically carries more current than normal cloud-to-ground lightning". The diagram showed normal lightning bolts at about 30kA, and the rarer positive lightning bolts (electrons go from ground to cloud) at 100 to 200kA.