In my opinion, GIS.SE should keep the arcgis-desktop tag because it is public facing.
For example, when suggesting the user to be more specific and add tags about the GIS software being used, it is more natural to think that one is using arcgis-desktop (vs qgis postgis etc.) than arcmap
In response to your comment
(it could be made a synonym of [arcmap]), ..., being public facing did not prevent confusion; redundancy with
My thinking is more of the opposite. In most of these cases about platform choice, arcmap would be the redundant one. It is natural to think of arcgis-desktop as the platform. arcgis is too big, because it contains arcgis-server too. arcmap .. just isn't a platform. Merging arcgis-desktop into arcmap seems bizarre here.
I'm not sure what you mean by being purist. I share the same unease with you about
ArcGIS Desktop is their flagship product's name, but within that they
have two flagship applications (ArcMap and ArcGIS Pro).
except that in my sense, ArcGIS Pro is more than ArcMap. Instead, it is equivalent to the old ArcGIS-Dekstop without the ArcGIS Pro. There had been rumors for quite a while that ArcGIS Pro will replace ArcGIS-Desktop based on newer technology etc.
Now in this situation where there are two overlapping subsystems (with separate version numbers) under the same suite, what should one call the "old" ArcGIS Desktop? If it's arcgis-desktop-classic arcgis-desktop-10.x, I can still think. If it's arcmap, it seems to be misconception to me (Maybe it's just me).
But of course, I'm not in a position to speak for ESRI about how they brand they products. And I don't think anyone can by deciding on their behalf that the old arcgis-desktop should now be called arcmap.
I think it has been taught for a long time ArcMap is one component of ArcGIS-Desktop, along with ArcCatalog (and once ArcToolbox) plus other standalone items. This is why I think it is bizarre to replace arcgis-desktop with arc-map (or another component).
Since this is a poll, I just wanted to express my personal view as a ESRI user.
I think the point that we should not confuse arcgis-desktop with arc-map is also discussed elsewhere: Should arcmap tag be a synonym of arcgis-desktop