Besides software and familiarity, I'm sure the Mini's form factor has a lot to do with it.
Also, if you need to replace or duplicate a unit with an identical one, you know you can always run out and easily find replacement Mac Minis. If you used some random ultra-SFF PC, can you be sure you can get another identical one easily if you need to? What about 3 years from now? Changing out hardware always introduces a possibility that something might go wrong - exactly what you don't want on a broadway show, a few hours before a performance!
Also, if you need to replace or duplicate a unit with an identical one, you know you can always run out and easily find replacement Mac Minis. If you used some random ultra-SFF PC, can you be sure you can get another identical one easily if you need to? What about 3 years from now? Changing out hardware always introduces a possibility that something might go wrong - exactly what you don't want on a broadway show, a few hours before a performance!