By the way, moving 'to the cloud' never means a specific thing because people have made words (intentionally?) vague to the point where you have to explicitly specify all the factors you take into account with your work in order to figure out which 'cloud' they had in mind.
Running a static workload doesn't require elasticity, but a 'cloud' isn't just elasticity. If you want "a program on a server with some storage that is always there" without having to deal with hardware, software, networking, storage, backup, maintenance, upgrades, service contracts etc. then an arbitrary virtual machine where someone else takes care of the rest makes total sense.