Does every professor need to do research? I wonder if there are some professors only focusing on teaching or management but no research. I think this may be feasible.
In the Netherlands you can have a "buitengewoon hoogleraar", who has a professor position of typically one day a week and another position somewhere else. Often this is an external entity like a company, but this has also been used to give a professor title (but not the pay) to someone who does the managent of some institute.