Most of my reasoning behind initiative is spot-on with Rob's.
Asking everyone to roll for initiative is a great and subtle way of telling the players to pick up their dice, because this is the part where their characters are going to die. There are times when I--or a player--want to initiate an attack without the Final Fantasy screen flash. The (sort of) mechanic used in this instance is surprise. If the target had no way to know--for example--that a crossbow bolt was going to come shooting in the window while he was on the toilet, then he cannot defend against it. Just roll for the attack alone, without initiative or other rolls being involved.
Midian's initiative system determines when someone acts, and how often. Actions are resolved right then. This speeds up both the resolution time as well as sometimes adding the tactical decision of act vs. wait. Randomness to the initiative rolls--often determined every round--add to the general chaos of battle. This keeps the players on their toes. They aren't as likely to wander out of the room as they would be if they know I always have six other players to handle between their actions. This also helps keep the outcome of the battle itself uncertain. Everything a player-character can do in Midian's combat engine only pushes odds in their favour; nothing guarantees success. Just entering combat means your other means of resolving the situation have failed, and now your life is in jeopardy. Keeping things hectic and a bit crazy reinforces the notion that you should try to find other ways to resolve conflict first.
Combat--like chess--is often won by whomever makes the next-to-last mistake. Going earlier, and more often, than your foe can rob him of the opportunity to correct a prior error, or to capitalise on one you made. Actions affect other actions, so initiative in Midian fits a more classic military definition than simply being who rolls dice first. That is, striking your foe impairs his actions against you, hinders his defences against your subsequent attacks, and reduces his next initiative roll which further impedes him. In other words, it is important to gain and retain the initiative in battle, especially if one wants to press the attack.
To add to tactical decisions--instead of just modifying dice rolls--other mechanics come into play. Some actions automatically place your foe after you in the initiative order or at the very end. Interrupts allow a character to skip ahead to pre-empt another character's stated action.
I am a quick-moving guy. I have scary fast reflexes. This affects my personal preference for game systems that favour such. It is also easier for me to envision--and design for--this type of combat schema. Mostly though, I really liked how Shadowrun handled initiative. I crudely hacked it into an act-now type of system and used it for my own purposes.
For what it's worth, everything I have read on the subject suggests that action is slower than reaction. That seems counterintuitive, but reflexes are faster than forebrain thought.