Since this subject involves my areas of specialization in Support Services, I have to wade in. One of the very common workflows Esri customers are involved with is bringing in CAD data - AutoCAD and Microstation - and overlaying or converting these data to GIS formats using tools available in Esri software or extensions.
In many cases, CAD data is created in a known coordinate system that has a WKID associated with it, and it that is the case, that's great. However, a lot of CAD data is created in an undefined local coordinate system, that has no relation to any known projection. In order to integrate these data into the GIS, the alignment issue has to be resolved one way or another. Here are the available methods.
1] Georeference the CAD file in Esri software (ArcMap or Pro). I do not advise customers to use this method, since georeferencing survey grade data changes the lengths of lines, and alters the angular relationship between those lines. Picture this with parcel data in a CAD file.
2] Create a custom projection file to align the data with reference data in a known projection. The custom projection file tells the software the location to draw the data on screen, without altering the geometry of the features. Chapters 4, 5 and 6 of my book "Lining Up Data in ArcGIS: a guide to map projections (Third Edition, Esri Press 2018) outlines this process in detail.
The other common occurrence with CAD data is that the projection is defined, but defined incorrectly - i.e. data created in a local coordinates then defined as State Plane for example.
Allowing the user to "clear" the projection from the data frame, either in ArcMap or Pro, is the single quickest and easiest method to determine if two data layers are actually projected to the same coordinate system. Do the coordinate extents of the data match, so that the data line up in an data frame with no projection assigned? If so, they are in the same coordinate system, regardless of the projection definition, which in any given case may be right or wrong.
In an ideal world, this would not be necessary, but we do not live, work, and do our GIS projects in an ideal world, so we need all the tricks available in order to make things work as efficiently as possible.