> "whatever you come up with will have a higher likelihood of failure"
This is where you are simply wrong.
> "the authoritative copy goes into the cloud"
This we agree on.
So, where you are wrong is this: you are only considering technical failure modes but there are many others besides and so any comparison between 'the cloud' and 'your get-out-jail-free-card-backup' would have to be in terms taking into account all modes of failure, not just the technical ones and then on top of that you'd have to consider the likelihood of the backup failing to restore at the same time that the primary system goes down for whatever reason (including technical ones).
That's why I call it a blind spot, even after being told in 20 different ways that the uptime of Amazon does not come into play here you are still clinging to that. It is simply not relevant because that's not the scenario a back-up will most likely prevent against. It will also prevent against that scenario, on top of the ones where someone incapacitated by drugs, anger, depression or any one of another set of circumstances decides to take it out on your company. Or maybe someone makes an honest mistake (I've been called out twice in my career to restore data for companies that had been wiped out because of simple mistakes that should have never ever happened).
So back-ups are not a luxury, they are a necessity and the degree to which Amazon can outperform your back-up in terms of availability is not a factor in the whole discussion.