This is a very cool idea, and there are already machines which do a similiar thing.
The main issue I see is that the forces are very different, you will need powerful stepper motors and strong lead screws/frame for a CNC mill/router as there is a significant loading, and these motors will end up being too slow when you need to print/engrave/cut.
Also you should really add a section about what materials people want to work with, I understand that your Laser Cutter will probably only be able to cut wood/plastics. But with the CNC mill, for FRC teams( and me personally) they will want to be able to work with aluminium and that isn't going to work if you have a little 775 motor as your spindle as many compact Chinese CNC's do.
Also the size of build area that you would normally see on a 3D printer( lets say 8x8) is kinda limiting on a Laser Cutter and router/mill
For personal use I would much rather buy 3 seperate machines cheap from China, then purchase one little machine that does all 3 terribly.
If you guys want some ideas you should look at the Sienci Mill:
http://sienci.com/