The question is: Does it make sense to build a combined 3D printer and CNC? It seems that despite the similarities in 3D printer and CNC, there are a few important differences.
A CNC needs to withhold a lot of lateral force from the mill head, so the mechanical structure needs to be build rigid and solid. That means any CNC machines are probably a bit heavy. On the other hand, a 3D printer only needs to move a relatively light print head, and therefore does not need to have that rigidity and mass of a CNC. A 3D printer needs to move fast, so one can use a thinner slice to achieve a better finish. That means a 3D printer probably want to be lighter.
A typical precision on a hobby CNC frame is probably need to be in the order of 1/1000th of a inch, or 1/100th of a millimeter. 3D printers, on the other hand, have nozzle size of 0.35mm or 0.5mm. That means the precision of the mechanical frame need not to be better than 1/10th of a millimeter. That is an order of magnitude different from the CNC setups. The lesser requirement on the mechanical precision means that the frames can be built lighter, and therefore can be moved faster (which is what the 3D printers need).
It seems that it makes little sense to combine these two. However, most of the sub-$1000 3D printers in the market has terrible precision. A more rigid (but not overkill) frame would definitely benefit the printing quality. Also, for a lot of hobby CNC works (especially on wood), a precision of 1/10th of a millimeter would be sufficient. So if such a compromise can be achieved in design at the right spot, maybe there is a room for such a combined machine. After all, it offers the benefit of saving the space in a garage workshop and space is always at a premium there.
After some research, I found this project called EasyMaker on the Internet. It seems to be a pretty interesting project that combines CNC and 3D printer.