Sit inside an airline cockpit once in a while, the majority of planes cannot do what a G1000 can.
Charts absolutely are used. On an approach, both pilots will have the approach plate (paper or otherwise) open and able to reference during the procedure.
The FMS, btw, is not why a B747 can execute a cat III landing. The aspects to that include crew certification (have to do a bunch of stuff in a sim to get certified), crew training (special procedures between the pilot flying and pilot not flying to setup the avionics, monitor the avionics and make the land/go around call), aircraft certification (there are extra sensors and instruments on the airplane with painted critical areas around them that must be free of dents and irregularities on preflight; the flight computers do more sensitive inter-comparisons between all of the instruments, the localizer is tracked with more sensitivity, radar altitude is used rather than pressure altitude), and airport certification (specific lighting systems must be installed and used, and the localizer and glideslope must be usable to the surface).
There is a lot more that goes into being able to fly and actually flying a cat III (my plane could only do cat II, but the concepts are the same) than just programming an approach into the FMS and engaging the autopilot.