You want mainframe in similar situations as when you need EC2 ridiculously large instances. That is when you have workload that absolutely most run as a whole on one big single machine. Typically that means OLTP database which cannot work with some relaxed consistency model (payment settlement is often cited example of such thing).
And for the elasticity part, mainframes are where the whole virtualization and hypervisors started. Although, or maybe because, purchasing and operating an mainframe is significant investment in terms of both capex and opex (it is somewhat telling that IBM's specification sheets for mainframes read somewhat like flyers for new cars, about half of the thing is about available financing methods :)).