I have had several times when it was necessary to reinstall WSUS on a SCCM server, you can do it and it is not a very complicated process. But the last time I did it - on a Windows Server 2012 R2 box and SCCM 1606 after reinstalling WSUS did initial sync and then failed.
In addition to it I saw 100% CPU usage for 10-15 minutes and then it stopped, also causing WSUS service to stop.
The problem for this is that WSUS initially has lots of request to process and lacks resources. So you have to configure WSUSPool application pool to have enough resources. Follow these steps:
1. Open IIS Manager;
2. Go to Application Pools, select WSUSPool
3. Select Advanced settings
4. Modify these values to
Queue Length = 3000
Private Memory Limits = 7843200 or 0 (which means there is no limit)