What I can confirm is that there is no random factor with the exhaustion effect. I can't go into details of the mechanics of it, but bear in mind that the exhaustion feature was implemented exactly to combat the small roster teams, and, we believe, in that it has had a very positive effect.
On the other hand, just like with all the other changes in the GE, it's probably not perfect and can have unwanted and unexpected side-effects, especially in specific cases. Since the largest majority of teams only use "follow depth chart" substitution tactic, we generally test changes with it, rather than the other options. In this case, you might have some unexpected results due to that specific setting, but it's just a feeling at this point. If it happens more regularly we can test this out more (in case you decide to keep using "coach picks from depth chart").