In radio and TV land these are called patch panels. I designed a number of stations and yes, I did always include them.
But they were for emergency situations or times where something unusual happened and the normal electronic routing equipment was not designed or installed for that unusual task. Or for maintenance purposes when test signals had to be inserted or readings taken at various points in the system.
For normal day to day operations, audio and video was routed with electronic switching systems, often following parallel paths. However it was common practice to install patch panels at the inputs and outputs of those electronic routing devices. This allowed things to be re-configured when unusual events occurred. These electronic switching systems were installed in a central location, taking up a significant amount of rack space. A video or audio signal only needed to be brought into them at one input in order to be available at any or all of the outputs which went to different locations in the station. Even audio mixers were primarily used when programming was being created or at the location where the on-air feed was being sent to the transmitter. They were not normally used for routing the audio to different points.
Patch panels were a bit of a maintenance problem due to the mechanical contacts. Many stations had a regular maintenance routine where they were "exercised" by inserting and removing patch cords multiple times to break any corrosion that may be forming on the "normal" contacts. Electronic switching equipment is far more reliable.
Music production is another thing and the facilities are often allowed to just grow when the musicians acquire different items of equipment. Audio mixers of course are more important. But the musicians are not engineers and things can grow into great tangles. I have seen recording studios where audio cables are run everywhere and someone simply goes behind the equipment and moves them around when needed. I have seen some real messes. Sooner or later someone decides to hire an engineer, perhaps on a part time basis, and then the facility starts to grow up.
Similar method served the phone companies
Not just telephones,it was also widely used in tv,radio and music production to route audio and make rerouting simple