When you are fatigued your balance will suffer....

Interesting but perhaps obvious.  When your muscles are fatigued your balance will be poorer.

Effects of exercise-induced fatigue on postural balance: a comparison of treadmill versus cycle fatiguing protocols

This is something important I believe in terms of injury prevention, particularly in walking.  When we are stronger, fitter and walking more efficiently (all covered in Hillfit) walking will be less fatiguing and  so balance will be impacted less.  You will be a more resilient walker, less likely to stumble, less likely to fall and get injured.