As Dknguyen says, the joysticks would be relatively difficult/expensive to build alone. (dunno about zigbee, wireless mesh networking seems overkill ;-).
Another huge advantage of off the shelf is, the mutichannel recievers are incredably tiny, and interface directly with servo actuators. To do all the transmitting/recieving and servo control would be quite a project. Interesting though, depends if thats the part that you want to build, it would also cost FAR more than off the shelf. I think youll find the mechanical building of the car woud be satisfying in itself.
As an aside, I built a remote control car-on-a-track with a videocam fitted on it in my music studio, using a butchered RC car ( well 2 actually, choped in half and the 2 drive ends bolted together for more power), on a track running near the cieling. Servos controlled the cam pan/tilt, and were contolled via the controller outside the studio with a video monitor (there was also a video RF transmitter on the car). The resulting video is here
YouTube - Low Profile
Video was taken slow/fast, rwd/rev and some handheld and edited in premier 6. The videocam stability feature came in handy ;-). (Im playing bass).
Corny, but shows what can be done with toys on a $2 budget the pros pay megabucks for with pro gear (if thats even possible in a tiny performance space).
A Cocacola exec saw this, and wanted to talk more about use in an add, but ofcourse it didnt come to anything