No technology can compensate poor planning and technical incompetence. From all I read that was the root cause of the problem. So the same people and processes using Kubernetes: No.
(Of course this is just speculation. I have no insider knowledge.)
Without even having got around to reading the whole report yet, I can promise you that a f*ckup on this scale cannot be avoided solely through technology decisions. The problem was (is always) with the people and the structures they were working in.
To the contrary, switching to a new technology is a favorite reductive excuse of poor management. They choose one early technical decision and try to hang all the failure on that.
As a sibling comment states a screw up of this magnitude is never simply a technology issue — it requires bad management at many levels.
Kubernetes are to help you scale. They do not fix one's incompetence. They increase complexity of the stack and if anything would make it even worse for the incompetents.
(Of course this is just speculation. I have no insider knowledge.)