Where it does make sense in the short-term for this scenario is the experience and knowledge necessary to reliably run your own servers. If you don’t have that, you may not want to invest the time and effort to do so. But on pure cost, unless your bill is on the order of a few thousand per month, cloud will never win. It can’t; they have to make money.
One justifiable excuse is you simply don't know how much hardware you will need to buy if you're hitting hockeystick growth. That until you realize you can also go hybrid...
You're right that if the longest window is short enough to make autoscaling financially beneficial over managed hosting, then you also need to make sure that you don't regularly have other spikes that can tip things back to being unprofitable.