I put my personals though on this topic, even that Martin and André have deeper knowledge in Dynamics AX than me.
If you goal is to move Dynamics AX servers to a on-premise solution, you should also consider an asynchronous system architecture between your web shop and Dynamics AX
If you take quick look to Microsoft Dynamics AX Online Shop or Retail architecture technet.microsoft.com/.../dn463983.aspx
You will find that most interfaces are not online with Dynamics AX, on that way, you can reduce hardware pressure in Dynamics AX, even if the AOS is down (planned maintenance, system crash, etc.) the online store will work properly except for viewing posted invoices.
Dynamics AX isn’t a bad solution, in the last 15 years I have worked with several ERP’s, including the leading ERP and I can ensure you, that most likely AX is one of the most flexible and powerful ERP’s. In the most failed implementations that I have seen there were some bad partners.
If you have your development and testing environments in Azure, You can move it to your private cloud solution, some customer use Azure only for their live systems.
Azure as a cost, but isn’t expensive if you are comparing to build by your own a high availability system.
If you feel that hardware is oversized and there any to many free resources on servers you can shut down some servers.