The big problem with the on site method is whether or not you can "eyeball" distances on varying sites. Some can do it better than I. I have stood on potential tees, looked to a nice LZ landform feature, and then measured and realized it was about 1000 yards away, not 300 yards.
Also, as I have said before, on tight properties, its often important to study how to use the perimeters first, just to fit the course in. And, if its a housing project, then there are lots of extraneous considerations with the land planner that are probably best roughed in via topo map, subject to change in the field.
I often use the phrase "miles, yards, feet, inches." Putting the holes in some general config on a big site often requires plans - the miles. Usually, the field walks move them yards in either direction, although, big changes sometimes result from the field walks too. In clearing or early construction you can still move things by many feet. After basic shaping has taken place, its down to inches you generally tend to move things. Of course, there are famous examples of big name architects moving things well after construction has begun, or even after irrigation has been done. Sometimes this has to be done, but its not real efficient or cost effective.
In general, I always thought the gca got paid in large part, not only for a good final result, but an efficient one as well, i.e. plan it out before construction so things can go smoothly. Its generally what architects do, even if the changes are what seems to be celebrated the most in news accounts.