The other way around. The cost to use Amazon never works out once hit more than a handful of high workload systems. I write out the proposal for our C levels every quarter and the increased cost of going to Amazon is enough to hire 2 full time level 1 sysadmins.
Edit: This obviously is super variable. If you have a low load worldwide need AWS will win. Or rapid bursts of traffic. Or hundreds of other scenarios where it makes sense. It is not a one size fits all solution though.
It depends on how you measure and account for cost. My last big on premises project landed about $10M of hardware, which wasn’t at capacity for about 18 months for various reasons. And that was a very successful project.
Yet it wasted about $2-2.5M in hardware value alone. That’s not free, especially when you wouldn’t be incurring cost on a pay by drink cloud model.
AWS works better and cheaper for almost everything that involve more than a rack of hardware.