In practice, that's not true, and it's not true enough to ruin the entire rest of your calculations. For Amazon regions to function independently, they'd have to be actually, factually independent; there is no interaction between them. The reaction to one node going down is never to increase the load on other nodes as people migrate services, etc. There's fundamentally nothing you can do about the fact that if enough of your capacity goes out then you will experience demand in excess of supply.
If you want true redundancy you will at the very least need to go to another entirely separate service that is not Amazon... and if enough people do that, they'll break the effective independence of that arrangement, too.
(This is a special case of a more general rule, which is that computers are generally so reliable that the ways in which their probabilities deviate from Gaussian or independence tends to dominate your worst-case calculations.)
After today's event, it would certainly be interesting to see how resource consumption changed in other availability zones and at other providers during this outage.
I wonder if that could be measured passively? What I mean is, by monitoring response times of various services that are known to be in specific regions and seeing how that metric changes (as opposed to waiting on a party that has little-to-no economic benefit to release that information.)
Of course, redundancy doesn't set itself up, so there are added costs on top of Amazon.
If expanding to another region costs more than just taking the outage, then it's categorically not a good option. If management still says no in the face of numbers that suggest yes, then that tells you that you're missing a hidden objection, and how you proceed will depend on a lot of factors specific to your situation.
Not complex even factoring in reputational damage?
In businesses where physical goods are sold to customers, "the management" is generally very motivated to avoid stock-out situations in which sales are lost due to lack of inventory (even if it's only a very small percentage.) The reason for this is because they are concerned about the potential loss of customer goodwill. It seems that the same applies in this situation.
let P(region fails) = 0.05% and let's assume (and hope) that the probability of failure of one region is independent of the state of the other regions.
P(two regions fail) = P(one region fails and another region fails) = P(region fails) * P(region fails) = 0.05% * 0.05% = 0.0025%
Making your availability = 100% - 0.0025% = 99.9975%
Ultimately it's more of a business decision if you want to pay for the extra 0.0475% of availability. I would think (or hope) that most engineers would want it anyway.
The numbers at this size appear insignificant. How would one (say an engineer) convince "the management" that the extra 0.0475% of availability is worth the investment/expense?