Organizing a game can be very difficult, particularly if it's not an athletic game-like sport. Even sports need designated turns, such as when playing a game like Golf, or changing ends in a game of Soccer, or doing a take-over on a relay. Even games like Soccer and American Football start and stop, trading the roles of the teams/players. In a sense games need to be ordered in order for them to make sense as games, with a beginning, middle, and ending. Board games, and table-top war games, are not different in kind.
Typically people either take turns making choices in games, or they make those choices simultaneously, and reveal their choices to determine the end-result of both decisions. Some games, like Poker, mix it up by having some choices made simultaneously, and others made in order. But player choices are just one part of the choice event. There are the game elements which will be affected by the player's atomic choices. In games like Chess, the player's choice directly affects the position of one element, one piece, at a time. Conversely, a player's choice may affect their opponent's choice. In Chess, moving a single piece makes each turn, each decision, a matter of both choosing between pieces to move, and choosing how to best affect the opponent's response.
From a non-strategic perspective, games are more engaging when players feel that they have a range of live options to choose from, as well as a choice to make, and when feedback from those choices is more immediate and controllable. Ideally a game should do what a player wants it to do. Practically speaking a game needs to manage a player's expectations of what their decisions will achieve, and how these decisions will achieve those expectations.
These perspectives can come into conflict. Designers can fail when strategic players want a non-trivial problem to solve, and non-strategic players want a game simple enough for them to follow. So it's important for a person designing a table-top war game to figure out how these players can meet in the middle and enjoy playing with each other. Sometimes designers will want to bite the bullet and simply design for one group or the other, but in general I think such restrictions are just that, post facto excuses to rationalize bad design decisions.
One way of engaging with this problem is to make a basic set of rules and then an expanded set of rules, either by writing core rules and layering expansions on over them, or writing a complete set of rules and extracting an introductory version from them. In the former case game development can see the original basic set of rules being either invalidated, or simply insufficient to support the superstructure expansions. In the latter case game development can be a case of discovering how little foundation the introductory rules give to the complete structure.
The way to solve this problem is not to sit down and start writing, but to break out the models, the dice, and every gaming aid and implement you have available (as well as some paper, scissors, glue and other artsy-crafty stuff to make gaming tools on the fly) and to play with it. I believe strongly that a design needs to achieve an equilibrium between the beautiful image of the game in their heads, and what is actually fun to do with toy soldiers, and that good designs result from both the codification of play into rules, and the testing-to-destruction of playing those rules competitively.
The question a game designer should be asking themselves is not how they want to design the turn sequence of their game, but how taking turns makes the game a fun and enjoyable past-time. As much fun as writing rules may be for the designer, a rulebook is a use-document, something that players pull out because their experience with the game has yet to be internalized, or the game is too complex (or too ad hoc in design...) to play from memory.