For all of those courses that state their course is unwalkable and a cart really is necessary, I offer Andrea Messer.
Due to rain delays she was left with 27 holes to play on Tuesday at the Women's Am. Carrying her own bag, she qualified for match play. Then yesterday, still carrying her own bag she won her first match on the 27th hole.
54 holes, carrying and walking, on a spread out course, heat in the mid-90s, and she was still able to play excellent golf.