Not a counterargument per se, but an observation: yes, initiative can get more complicated pretty quickly, especially if the players are declaring a lot of conditional actions. (That's actually pretty much the main case where I ask for initiative rolls, is to figure out whose conditional action is going to do what.)Yeah, intuitively this type of system sounds to me like it will require a bit more "work" on the part of the DM to keep things flowing correctly. Initiative can be clunky, but it's also fairly divorced from any key DM adjudications and can even be handled by a player if needed. Not the case here, I think.
I have a feeling Hemlock may have a counterargument, though.
On the other hand, separating action declaration from action resolution lets you offload work on the players. You can have one of the players keep track of the action declarations to make sure everyone declares (having that action declaration log in written form can also be useful for other purposes, such as establishing that "Thok, you can't cut the ropes tying these two ships together before you're busy attacking the Umber Hulk, remember?", especially if Thok's player is the one keeping the log) and you can also do action resolution concurrently: have players roll their attacks/damage as soon as they are ready, just as long as they don't announce them to people who haven't declared yet.
Ultimately I suspect that the total cognitive complexity of the combats you'll have under this system is somewhat higher than it would be under cyclic initiative, but it will be because the players are doing more complicated and IMO more fun things, like trying to tackle the Wolf before it can eat Peter.