A team does not use AWS because it provides compute. AWS, even when using barebonea EC2 instances, actually means on-demand provisioning of computational resources with the help of infrastructure-as-code services. A random developer logs into his AWS console, clicks a few buttons, and he's already running a fully instrumented service with logging and metrics a click away. He can click another button and delete/shut down everything. He can click on a button again and deploy the same application in multiple continents with static files provided through a global CDN, deployed with a dedicated pipeline. He clicks on another button again and everything is shut down again.
How do you pull that off with "Linux on-premises server administrators"? You don't.
At most, you can get your Linux server administrators to manage their hardware with something like OpenStack, but they would be playing the role of the AWS engineers that your "AWS administrators" don't even know exist. However, anyone who works with AWS only works on the abstraction layers above that which a "Linux on premises administrator" works on.