This keeps being brought up since the early days of AWS. Yes, the cloud is more expensive. It simply adds another layer of management, scalability, and flexibility you would not be able to build yourself. And there is a layer of profit for the cloud provider as well. Whoever was told the cloud would be cheaper was being lied to.
I've built cloud, colo'ed and hybrid systems. Every few years this would come up. Now, so many cloud services we use are connected to the cloud providers we don't even need to spin up SSO/authentication servers because it's simply built in at this point.
Something which sometimes gets lost from a US centric perspective is that cloud lets you get servers much closer to the end user without having to establish relationships with hosting companies and colo facilities on another continent. Shaving 100ms off of each request can be useful in a lot of circumstances.
And if latency is important, you need that origin to be close to the user.
The front end is the least latency critical component in a lot of stacks, because the user downloads it once and can cache it on their machine, whereas every single action they make using that UI is subject to the latency of going to your back end
I've built cloud, colo'ed and hybrid systems. Every few years this would come up. Now, so many cloud services we use are connected to the cloud providers we don't even need to spin up SSO/authentication servers because it's simply built in at this point.