For modern applications the premise of this story may be somewhat true, but for the world's banks, insurance companies, and governments, the mainframe will remain where it is at. Why? It's very simple. IBM mainframe operating systems are completely backwards compatible with the very first iteration of DOS/360, released in 1966 and IBM mainframes are completely hardware compatible with the first 1965-era IBM 360 mainframes. In short, you can run programs written in 1966 on the most modern IBM mainframes without recompiling the programs and they will work exactly as before with the one notable exception that they will run several orders of magnitude faster. The 64-bit Intel (and AMD) CPUs can execute anything from the DOS era but no modern operating system will support it. The same can be said about 16- and 32-bit Windows apps given that support for those has now been removed. MacOS? Nope. Linux? Nope!
Now, in theory, you could install the Herclues emulator in the could and run your mainframe apps in the could but I wouldn't recommend it. Hercules emulates the IBM instructions, meaning it's much, much slower than Big Iron. Keep in mind that modern IBM mainframe CPU's now run at 5 ghz. Also, you might have trouble getting access to an operating system to run on it. Older IBM mainframe operating systems are in the public domain and those can be used for many legacy tasks but if your newer apps require features present in a modern one, you're out of luck because IBM is not going to let you keep it in order to run it on a competitor's environment.
In short, if you are a company or an organization with a large software code base and you've been using mainframes for your computational needs, cloud computing does not offer much of an incentive to move to it.