I like the idea of dynamic initiative system depending on the situation. I have played with the thought quite a bit myself. The main deterrent I have found is that rulings with regard to which system to use might be of disproponate importance to players with characters that have taken features that changes initiative. For instance if a player has chosen a feat that allow them to use wisdom instead of dex when rolling initiative, the value of that choice is highly diminished if this choice only matters in climatic fights. Moreover that player might be prone to argue that fights should be considered climatic, or ask for more climatic fights.
By having a consistent initiative system up front that ignore or significantly lessens the value of initiative modifying features up front, the players can chose to avoid them, or have made an informed chase if taking them anyway, rather than feeling cheated if it turns out it never come into play.