The computer does fly most of the approach, however control is usually given to the astronauts once the shuttle has slowed below supersonic speeds (shortly before flying the heading alignment cone, I believe) and the entire approach and landing sequence is usually flown manually, the computer does however supply guidance to the commander to keep him on the glide path. Flying the landing by hand is entirely feasible, what isn't feasible is flying the landing by hand without some kind of guidance from the computer, as the glidepath, descent rate, and speed that the shuttle is flying makes it virtually impossible to manage energy properly to arrive over the end of the runway with proper speed/altitude.