A Power BI Report with an ArcGIS map can be shared using the Power BI web app's "Publish to Web" function, but the the ArcGIS visual does not show, instead there is an error message indicating that this is not available.
Every other visual that is part of Power BI's core visual list (as the ArcGIS Map now is) can be published in this way, as can any Custom Visual. The only exception I'm aware of is the ArcGIS Map.
When will this be resolved?
This is horrible! I had to balance a lot of issues in choosing between Tableau and PowerBI for creating a public dashboard. If I had known the ArcMap option was not available when publishing a report to the web I would have chosen Tableau. This is incredibly frustrating.