I'm posting this as a discussion in hopes of helping someone else that encounters this same issue. I have already found a workaround so this is not a question.
I'm using ArcGIS Desktop 10.5.1 trying to enable editor tracking on all feature class datasets in a 10.5.1 enterprise geodatabase.
The datasets are all registered as versioned. They also all have archiving enabled. I am connecting to the database as the owner in ArcCatalog 10.5.1..
If I right-click a dataset, choose Manage and click Enable Editor Tracking, it will succeed using the default field names, create fields if they don't exist, and save times in UTC, none of which works for our situation because we already have fields for last edit name and date which have been populated by a custom ArcMap extension. Nor do we want UTC time. Because we do not want the defaults, I've tried every possible way to use the Enable Editor Tracking tool but it always throws "ERROR 001216: Editor Tracking not supported for dataset blah-blah". This is not correct because the geodatabase version is 10.5.1.
The workaround, which is not discussed in any ESRI Editor Tracking help pages that I could find, is to use the Editor Tracking tab in each feature class's properties page. There I can successfully set the tracking fields and set the time format. Rather painful for lots of feature classes but the tool does not work for me.
Hope this saves someone the time it cost me to figure this out.