I believe you would. Anyone would. Body didn't just stop working when you run faster or longer, body gradually develops pain. When you start to feel it, it feels not as a pain, but as a discomfort, which gradually becomes stronger, then it becomes pain, then it grows to an unbearable level. If your running/walking abilities were lower than they are, you would walk slower, to keep the same level of discomfort.

> Lots of animals can walk long distances just fine.

Not like humans. Humans walk faster than most of animals. As I understand it, it is due to aerobic ability mostly, human could absorb more of oxygen per minute and use it to oxidize glucose or fats to get ATP to power muscles. Other animals could absorb less oxygen per minute, so their body could output less power for a long time. Horse have 1 hp, but for relatively short amount of time. Then it needs to rest. Human could catch up with a horse before it managed to process all the lactic acid accumulated while horse moved (it needs oxygen to process lactic acid into ATP). This way human could outrun (or even outwalk) horse. (Maybe not the modern human with a car spending most of his day in a chair, but modern human have a car, so he could move faster than horse and for longer distances. So it does not counts.)

Though maybe it is not just aerobic ability, I think. Horse eats plants with a limited density of energy, it increases mass of horse, making it less energy efficient than human who eats foods with higher Kcal/gramm.