Mainframes are still the best option for systems that cannot fail. Even business like FedEx is not as critical as some types of business I've seen ran through IBM.

A good example of where these systems come into their own is payment/ACH/wire processing. The consequences of these networks going down are so severe that it is worth it to construct an entire facility with the computer systems and business in mind from the very beginning.

Today, mainframes are more for the type of business that are finding the need to pour the literal foundations for their own datacenters. If you are even considering cloud as a viable path, then this kind of stuff is certainly not for you.