Exchange 2013 powershell broken after server 'rename' due to certificate problem

Everyone knows you cannot rename an Exchange Server once you have installed Exchange on it.

In this example the Server needed to be renamed. Exchange 2013 was un-installed, the server removed from the domain, renamed then added back to the domain.

Exchange 2013 was installed again. I noticed that some Exchange directories under program files\exchange were not removed by the un-installation, but decided that MS knew what they were doing. There were several GB worth of directories. I pondered on what else was left behind...

Installation gave no errors, and the server was put as the member of a DAG and came up with some errors when the DAG was set up. Interesting... firing up PowerShell on the server in question gave a cryptic error and little else.
Runspace Id: 22b854a9-cbd4-4567-97b6-f3aa52c12249 Pipeline Id: 00000000-0000-0000-0000-000000000000. WSMan reported an error with error code: -2144108477.
 Error message: Connecting to remote server ex2.mydomain.local failed with the following error message : [ClientAccessServer=EX,BackEndServer=ex2.mydomain.local,RequestId=a34012f8-4b26-4ac7-9cb4-b57657fb9adf,TimeStamp=03/07/2014 16:31:29] [FailureCategory=Cafe-SendFailure]  For more information, see the about_Remote_Troubleshooting Help topic.

Deleting and recreating the PowerShell virtual directory made no difference.
http://technet.microsoft.com/en-us/library/dd335085(v=exchg.150).aspx

Then my colleague noted a strange event in the event logs:
An error occurred while using SSL configuration for endpoint 0.0.0.0:444.  The error status code is contained within the returned data.

This was more like it. HTTPS was pointing to a non-existent certificate - probably the original self signed certificate from the early installation, that was deleted during 'manual' tidying up. The new self signed certificate was bound and everything started working again.

I think next time an Exchange server needs 'renaming' I will un-install Exchange, then reinstall Windows from scratch... I doubt that much time is spent investigating problems like the above by the Exchange development team.