First of all, yes, people should be using multiple DNS providers for services that require very high uptime. Amazon.com itself notably uses Dyn and UltraDNS as

First of all, yes, people should be using multiple DNS providers for services that require very high uptime. Amazon.com itself notably uses Dyn and UltraDNS as its nameservers. That said, I'm not sure this would have helped in this case. It seems like some or all of the problem was internal Azure zones were failing to resolve. Which no third party DNS provider would be able to mitigate.