That is very odd and doesn't mesh with my experience at all. Usually the server cost is linear with growth (more or less) so if the per unit cost is fixed (more or less) then how on earth would such a swap occur.
Depends on the size. When operating your own servers, you need to recreate all that cloud providers do for you:
- maintain the physical machines
- build or rent data centers
- have people to operate, maintain, upgrade the machines
- set up, build, maintain, update, upgrade infrastructure for your projects to work on your machines
All these costs are not insignificant when you need more and more machines. And as it was mentioned above, they don't do well when demand is variable: when you no longer need as many machines, you can't just decommission them. When demand spikes, you can't install new servers instantly.
They’d why you do hybrid, baseline on prem.
At one point it's quite possible that a combination of the two is the cheaper option.
And yes, you're completely right, load variability plays a huge role in all this.