The dice pool success/fail roll sounds interesting, I would like to see it in action.
As far as the initiative question, I lean towards a more amorphous approach. Having a set order has its benefits, but I personally see more downsides. To me it has a tendency to grind the game to a snails pace. Players, especially in current times, have an attention span of just a few minutes (I'm not pointing fingers, I'm as bad as the next player), having to wait on each person to take their turn leads to players "drifting off". Especially if a player waits until the start of their turn to begin to come up with an idea, or if the action of the player before them completely changed the battlefield.
A looser, more open initiative leads to players acting when an opportunity arises leading to a more attentive audience, in my humble opinion. The down side is, if the group isn't looking out for that quiet player, that player could sit quietly by and have the entire encounter take place without saying a word if no one brings them into the action.
My favorite initiative so far, while I don't believe they are the first to come up with it, has been Daggerheart from Darrington Press. Theirs is a loose, act when you want style with play shifting back and forth between the players and the GM via failure. The players act, and will continue to do so until they fail an action, at that time play returns to the GM. It seems to keep a better balance of player action and GM action. There are more specifics, but that is the basics of their initiative system.
I fully admit I have limited experience as a GM, so I am far from an expert, but the system that allows the players to be more active and have a larger role in the pacing of the game is certainly the better choice for my style. Now will a loose system work for a Play-by-Post? That I have no idea. I can see many more problems with that style if everyone is not seated at the same table, or at least in the same timezone. Strauss and I can have an entire encounter wrapped up before Sabrina even knows there is danger if there is nothing holding us back. For games that have a delay of some sort would likely need a bit more of a structured system to work best.
There are certainly pros and cons to both styles I have mentioned, and like all things I'm sure some swear by one and hate the other, and I don't think that will change anytime soon. Each person has their own style of play that they enjoy, and initiative is just another part of that. The day that I find the perfect initiative that has no flaws and everyone loves I will be sure to let you all know!