I share that concern for my system work, and it is definitely something that requires playtesting. But here at least is the ivory tower theory crafting (and one practical example) for why it should work in this situation:
1. You are taking a whole lot of the complexity of the movement part out. This means you've got some room to add back in a bit of complexity to handle this aspect.
2. One of the reasons that round by round initiative can bog down in a 3E/4E style system is you've already got everyone rolling for a fairly narrow thing--the order everyone goes. That's all it does. That's why some people even house rule to just go on modifier, and why other games sometimes pick that option, too. There just isn't enough there to make it more complicated or involve decisions. So make it as simple as possible. But as soon as you expand the problem space to "movement + initiative", there are decisions to be made, and thus room for more.
3. This doesn't necessarily have to be round by round to still matter or be useful. See Burning Wheel, where the "positioning test" is a bunch of opposed rolls, then three "exchanges" of combat are made before another test. Not that BW includes character action order in the positioning test, but you get the idea. You might only force an initiative test when someone wanted to change zones, or more than one zone, or beat someone to a zone, or (by fiat) if the DM judged that the original situation had changed a lot. Or any number of things.
I think initiative is certainly something that should be a little more intrinsic to combat rather than the admittedly easier but less rewarding set and forget style of 3e/4e.
Some ideas to ponder of a semi-cyclical system:
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Initiative. Imagine that a combatant's initiative value is always important and represents how well a combatant prepares and reacts in combat. Skill is as much a factor as reflexes; for example quick reactions are important but skillful combatants tend not to paint themselves into corners.
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Order. You have your initiative value and that determines the order of combatants. You
do not roll to modify your initiative value. Every new round, everyone still goes in initiative order.
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Change in Initiative. Not often, but occasionally, a combatants initiative can change. If a combatant is dazed, they may lose 2 off of their initiative until they try to shake it off. If a combat is stunned, they may lose 8 off of their initiative as well as lose all their secondary actions (they can only perform their "standard" action - this has greater repercussions is you follow my standard/minor/multiple swift actions a round idea); again until they can shake it off. A slowed character might only lose 4 to their initiative but they cannot perform reactions.
However, there might also be ways of momentarily increasing your initiative such as if you ready at the end of a round, if you are hasted, or if you are critically successful in an action and thus spend a secondary action to push your character and get an edge in initiative. A leader might be able to increase his allies initiative at a critical point of a battle when he downs an opposing commander.
The important aspect here is that you are giving the "mundane/non-magical fighter" ways of reasonably affecting combatants that previously could only be achieved by magic or slightly far-fetched powers. You are providing another arena for the mundane fighter to excel at thus achieving balance between the fighters and the casters while maybe giving the casters a little of their mojo back.
- Movement and Initiative. If you want to do zones rather than formal concrete movement, I think the trick becomes that you want slower combatants declaring their movement first (and thus higher initiative combatants getting to react to that with possible opportunity actions as required). The higher your initiative the later you get to act (and thus get to put yourself in the choicest zone(s) with fewer people able to react to that movement). Not though that a defenders closing down of a zone still applies, even if the defender does not still technically have initiative on their quicker opponent. And so you effectively determine movement in
reverse initiative order. Once combatants have been "positioned" in their zones, actions are then performed in standard initiative order as usual. I like the idea of having multiple actions in a round where they do not need to be performed on your initiative turn but any time on or after your turn in initiative, thus delaying is always free and does not affect your initiative capacity.
The Discrete Round. What happens then is each round tends to be its own discrete thing. You still need to provide the capacity to have actions spread across these discrete rounds. This is usually done by dumping all your actions into an action (such as climbing up to a ledge), that then is not paid off until a subsequent round (the next round, you are considered to be in that "Ledge Zone").
Just some food for thought.
Best Regards
Herremann the Wise