No... what kind of "starter hero" rule are you talking about in Heroes of Might and Magic? It violates a basic tournament rule - playing with the same hero throughout the entire game.
You really love statistics, so calculate what percentage of games in Heroes of Might and Magic I have players using the starting hero (and keeping them as the main hero). This rule is violated by default because, in most games, the starting hero doesn't really matter in the end, it could even be a random hero. And what I suggested looks very interesting in the long run in Heroes of Might and Magic II: in the first game, you have your own starting hero, and your opponent has a random hero from your castle; in the second game, it's the opposite. Maybe this isn't a "starter hero" rule anymore because the Haven faction has some "deeper understanding of the overall idea"...