Hi,
Certain dataset in our organization requires to be only for display, query and identify purposes when shared to public. There should be a fine grained control on allowing or disabling data export from ArcGIS Map or Feature service. Currently, both map and feature services are designed either to be secured completely or shared to public for display, query or download.
The export function isn't obvious, but functionality is available as explained through https://community.esri.com/t5/arcgis-online-documents/download-arcgis-online-feature-service-or-arcg... or https://community.esri.com/t5/arcgis-enterprise-questions/how-to-download-extract-the-content-data-o.... Please note that there is an 'Extract' operation allowed on Feature Access capability https://enterprise.arcgis.com/en/server/10.8/publish-services/windows/editor-permissions-for-feature..., but it has a different purpose and won't change this behavior.
I will propose having control on making a map service open to public, but strictly following the OGC WMS service definition with display, identify, query capabilities as per the link https://en.wikipedia.org/wiki/Web_Map_Service. And it shouldn't be mixed with Image Service definition as it should be dynamic.