See my previous post for a full history on this.
In it, I had migrated from WorkspaceONE to Mosyle. One some devices I needed to clear the profiles database to be able to remove WS1 and enroll with Mosyle. When you do that the Profiles button in System Preferences goes away, forever.
Well, I did that one machine running macOS 10.14 and upgraded it to 10.15. Once upgraded, the profiles button returned! HOORAY!