You don't need Support Assist. It is not required so you skip the reinstallation. In fact, it can cause problems as you have observed. Check Startup on the Apps page to make sure it is not loading at boot.  Did you use Settings, Apps to uninstall it correctly? Don't delete anything. Uninstall it instead. 
SupportAssist became inoperative in a Windows 10 Insider build and I couldn't get it updated so I removed the program from my computer, making certain to delete all files related to SupportAssist. Now when I try to reinstall the latest version the installer informs me that SupportAssist already exists on my computer. I have searched all files on my Dell Inspiron 15-3552 laptop and can find no files relating to SupportAssist and it doesn't appear in the installed programs in Control Panel, or anywhere else I've looked. I can find no solution to this issue.
SupportAssist issue.