The latest release of Collector on iOS promises this feature, but when I tested it on a project (project was uploaded to AGO prior to the app update) no EXIF data is recorded. Is there anything I have to do in AGO or Collector to have this feature enabled?
I did somewhat, but it's not that straightforward, I had to export from AGO the feature layer that contained the points that had photo attachments as a file geodatabase, then using an export attachments tool (developed in-house) export the attachments as photographs and these photos had EXIF data, I verified this by generating points by using the 'Geotagged Photos to Points' tool.
As you discovered, there is no action required within Collector (or your ArcGIS organization) to support storage of EXIF metadata associated with the photos. While it isn't directly available within Collector, having that information at a later date can be useful for scenarios such as the one you mentioned.
Collector 10.4.0 on android - photo attachments when downloaded have the EXIF data stripped. Only when I develop another tool like Brian Cowper can I get the EXIF data back. Is that correct?
The Exif should be there there but you need to export the whole AGOL layer as fgdb, then download file geodatabase, then run a python script to extract all the attachments.. Yes it really is that cumbersome.
ESRI have a script to extract the attachments at:
How To: Batch export attachments from a feature class