Why did the Survey Corps search along the wall instead of on top of the wall to find a hole in the wall?
Well, it is true that you could spot a titan from the wall but, don't forget the time of day it was. Night, it was pitch black at that time. You might be able to see a 15m titan but a 3-4 meter is questionable. Yes it would have been safer to use the wall but at the cost of visibility. I don't know exactly but most of the titans that we have seen arent 15m tall. So they chose to go on the ground to maximize visibility.