So, as a refresher, the initiative system we're discussing here is this:
Phase 1: People using magic declare they are going to do so. Describe the beginning of the ritual/casting.
Phase 2: People using ranged attacks declare they are going to do so. Describe the aiming, nocking,etc.
Phase 3: People attacking in melee declare so, and then do so simultaneously.
Phase 4: People moving declare so and then do so simultaneously. (Helpful to have a speed mechanic here. I should also add that this is when characters who are using their turn for anything outside of combat or magic takes their action.)
Phase 5: All ranged attacks are resolved.
Phase 6: All spells/magic effects are resolved.
So let's explore the implications of this system a bit.
First of all, although it has phases, it clearly implies that all of this stuff is happening more or less simultaneously. Declaring actions is meant to draw attention to the fact that spells and projectile attacks can be interrupted before they occur. So although the aiming and chanting happens at the same time as the swinging and running, the magic and ranged attacks are not complete until after the melee attacks and moves have resolved.
So, if your sorcerer or archer gets hit in the face with a broadsword, that thing you were trying to do doesn't happen. No concentration checks or anything, all you have protecting you are your fellow party members, your strategic positioning during the encounter, and your Armor Class.
Since melee attacks are declared and then resolved immediately, they cannot be interrupted in the same way.
By the same token, moving can be done without any prep, so if a combatant wants to turn tail and run, there is no opportunity attack or arrow to the knee that can stop him before he starts (though that arrow may bring him down half way to his escape). However, if a combatant is going to run, it should be pretty clear after they do not cast, aim, or swing in melee. So although opportunity attacks are not part of this system, melee attackers can choose to wack the guys who look ready to flee if they so desired.
My system uses a "ganging-up" mechanic (largely based on one from Within the Ring of Fire), which replaces flanking for theater of the mind combat. Essentially, successive attacks against the same combatant in the same round of combat get bonuses to hit. This not only leads to cool combo moves planned out by the party on the fly, but it also gives a little bonus to those bow and javelin users.
Since all melee attacks occur before the ranged attacks, ranged attackers have their pick of the lot for targets. That goblin that your rogue and fighter just smacked upside the head but failed to kill? Well he's too busy to dodge your arrow, so you have a nice hefty bonus if you loose your bowstring in his direction.
Essentially, this system gives ranged attackers time to pick good targets. Shots that are "open," so to speak.
You might wonder how magicians fair in this system, since they essentially warn everyone of what they are doing at the beginning, and then only get to finish their spell at the very end. That would seem like a huge disadvantage. Because it is.
But, when you use that disadvantage and get rid of the usual ones, it balances out. In my system, there are no saves versus magic. There aren't even attacks with magic projectiles like a magic missile. If your spell goes off at the end of the round, it just works, no questions asked. The only option for combatants trying to avoid a spell are to stop it before it finishes, or get out of its area of effect.
All this talk is good, but let me run you through an example round to give you a better idea of how this would work:
The situation: You kick down the door to the evil cult's lair and just inside they have some poor guy tied to the floor above a pentagram, ready to be carved like a christmas ham. There are five cultists, two on either side of the would-be sacrifice, and another across the room, reading from a black tome of cult-y magics. The fight is on.
Phase 1: The head cultists at the back of the room flips to a different page in his evil book and begins chanting and motioning with his free hand. The candles lit throughout the room have their flames stolen and collected into a ball of fire the size of a watermelon at the tip of the cultists fingers. Slowly the fiery mass condenses and shrinks, burning brighter with each passing second.
Meanwhile, the party wizard pulls out a scroll from her belt and unfurls it, whispering in an arcane language and taking a few steps toward the pentagram.
Phase 2: The party rogue uses throwing daggers, cuz he's a bad ass halfling with a chip on his shoulder. He's about to pull one out and make a pin-cushion out of that fireball wielding cultist, but the party fighter says "I got this," and takes a javelin from his back. "You get that guy untied," the warrior nods toward that poor sap on the floor, and the rogue agrees.
One of the cultists pulls out a dagger and takes aim at the party wizard, but luckily...
Phase 3: The cleric takes notice and moves himself between the two. He uses his mace to knock some sense into that knife-totting cultist, who loses his shot at our caster friend.
Unfortunately for the cleric, two of the other cultists give him a run for his money, and their combined (melee) dagger hits take away nearly half the cleric's HP. Ouch, being outnumbered really sucks.
The last cultist goon takes his knife and goes to shiv the fighter before he can toss his pointy stick at their leader, but his pitiful attempt is sidestepped by our handsome warrior and the cultist tumbles out the broken door frame.
Phase 4: The rogue now takes his turn, cutting the captive free, who immediately scrambles for the door, though he doesn't get out quite yet.
Phase 5: The javelin flies through the air, piercing the cultist's black book to his chest and poking out the other the sorcerer's back. His ball of fire goes pifft into a wisp of smoke harmlessly. He stumbles backward, nearly dead.
Phase 6: The wizard's scroll glows a bright blue, and from its parchment an icy ray rockets toward the cult leader. His body freezes solid in a matter of seconds, and then falls backwards from the dais, shattering on the ground into a million tiny cult-cubes.
[Aftermath]: The other four cultists look back in horror at the effectiveness of the party, but know that if they continue their attack, they may take this cleric heathen with them to hell. The freed stranger cries many thanks as he continues toward the door. And the battle continues...
There ya go. Hope it sounds interesting enough for you to give it a try.