Here's a concrete issue I've come accross with this greyed out gizmo, if confusion and annoyance expressed by me and other users was not sufficient.
Can one tell what's selected in this image?
It's a null on the right side of the image, but could just as well be another object in the viewport with the pivot in that place.
If I'm placing nulls in a side view for rigging or other purposes and I want to set its display size to a certain value, I can't get any visual feedback about its size below the constant size of the gizmo, because the greyed out thing is on top. Not only do I have to select other object, I also have to activate a transform tool for that other object to get rid of that grey gizmo, and then switch to the select tool to come back to the wanted object
If the purpose of this feature was to know in viewport what object the active properties page belongs to, this is a plain uninspired solution to the problem.
A simple object color change or other type of visual aid (like small doted brackets, always facing the camera) are good alternatives IMO, because a grey gizmo, apart from the problems mentioned above, doesn't give you any actual info about what object was selected (has the active properties page) as many objects can have their pivot in the same place.
Cheers!