You can do this with excel, atleast if you approximate the design a bit. Excell is probably the only tool that a unspecified random crowd can be expected to be able to use.
The real problem is that the more easy to use, and the more mainstream you want to go the more you need to sacrafice out of your design.
Excel can be made quite faithfull to your idea but then youd need quite much work at the cost of usability and general understandability. The more you compromise the closer you get to the goal of ease of use. At the other end of the spectrum its easier just to illustrate this.
Image 1: Multilevel doughnut chart test quickly made in excel
Quite surprisingly the easiest software to do this in was when i tried was Autocad (or indeed any other parametric cad). Which the 3 random cad users found very easy to modify and i could get exactly your design in just 10 Mins. Hardly mainstream though.
To this end i would look for a software that can do geometric constraints based drawings i remember seeing one free soft of this kind.
The other option would be to make an app, mathematica or python + matplotlib come to mind. However im not so sure on easy to use this is. Certainly it could be made easy but thats a bit of work. I mean depending on users might be easier to learn Illustrator instead.
Image 2: A quick test in mathematica
Clobbering something together in python takes a few hours, but making it usable and distributable takes weeks. Consider web app with something like raphael.js. Easier to distribute.