If your service is mission-critical, you’ll have a support contract, and there absolutely is a number you can call. I have high confidence that Google and Amazon will make every effort to make sure their services perform to spec, the real problem is the feeling of helplessness when something does go wrong.
Of course you have a support contract, but how fast you can get a response still doesn't change. AWS Business Support - which is what is very common, a "Production Down" has a 1hr SLA for response. That's a long ass time for a database to be down without doing anything more than sitting on your hands.