I see this discussion has been running for some time, but jumping in to say that I too am an ArcGIS Pro user (just updated to v 2.6) who misses the option of clearing the map projection.
In Australia we've recently adopted a new national datum to compensate for continental drift that re-positions coordinates some 1.5m to the north-east. Further, there can be another 3cm difference in output values depending on which transformation method is applied to arrive at the new grid coordinates.
I've been doing some testing of Esri's transformation files using ArcGIS Pro and could manipulate the projection definition of the feature classes to get the result I want, but that seems counter-intuitive and could create problems later on if the correct projection definition isn't restored. So in the end it just seems simpler to bring the data into ArcMap to compare the various transformed datasets relative to each other and to see spatially the offsets - ie for QA purposes I deliberately don't want them automatically to align.
Further, as Margaret Maher has outlined above, my agency also often receives CAD data to be imported into the GIS and a quick, visual way to verify the coordinate system of the supplied data is very useful (a 1.5m shift is easy to miss and there will be plenty of non-surveyors among our stakeholders who may not even be aware of the datum change).
Maybe there's hope the feature can be included in ArcGIS Pro version 2.7?