Earlier quoted context omitted.
"Nobody runs Windows Server on the Cloud" is a massive stretch. It may not be a leader but it's definitely used https://www.datanyze.com/market-share/operating-systems/wind... Also if your stack is .NET you definitely need Windows Server. Even Amazon has some things built on .NET/Windows Server (woot.com)
.net core, which the flagship of the future, is cross platform. I am running it in ubuntu production environment for an App i made. Very stable.
The .net core project indeed runs fine on Linux in AWS. It's a great success story for us.
The ASP .NET projects I maintain have a budget that doesn't easily allow us to just migrate them to .net core. There are some hairy legacy libs and code in there that would also prove challenging to resolve too.