It makes sense when you aren't a datacenter hosting company as your core business.
Once you're done with your DRP and BCP it's highly unlikely that your server-under-the-desk (as it usually is) is worth the risk.
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.
And its easy to compare the cost of the cloud running your hardware to the cost of physical hardware. However, its much more difficult to compare the indirect costs between the two, and that's where I think many people go sideways.
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.