I don't think that the ESB is mission-critical to a company any more than any other "commodity" IT service component that does not constitute the core and proprietary business knowledge, expertise and data of the company.
Sure, an external (or internal) ESB total failure can take down the business for a while. So can a wide electrical or Internet outage, flood, fire, etc. Companies cannot and do not totally insulate themselves from all external dependencies. Moreover, unless you are responsible for managing a disaster (FEMA) the losses the business faces from widespread outages are mitigated in part by the fact that partners and customers are also likely affected and therefore even if your company is up and running, there's not a lot of business to be done. (My big takeaway from Y2K.)
As for the fact that AWS and other Cloud providers have outages: sure, but the relevant standard is not perfection but performance relative to alternatives. My impression is that Cloud providers, at least the leading ones, measure up well by that standard.
Martin