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==Overview==
The I-go-you-go system is simple but has the drawback that one player does most things for a long time while the opposing player waits for a good while. The only options available to a player down-turn (barring dome specials like Warp Spider Movement/etc) are:
"Do I attempt to Deny?"
"Do I Jink/Go to Ground?"
"Do I attempt Overwatch?"

Another thread on here talks about alternating unit activations. However, 40k is the sort of game where there's enough variance in unit-count (a unit could either be a Guard Platoon or a single Spore Mine) that a clean implementation is easier said than done.

==Proposal==
A turn in 40k consists of three phases: The Movement Phase, The Action Phase (Shooting, additional movement, non-combat actions like repairs, etc), and the Assault Phase (Charges/overwatch/etc). Psyker Powers are something separate I'm contemplating; they might either go in the Action Phase (aka merged with the Shooting Phase), or be split throughout the turn.

For each Phase, one player is said to Hold The Initiative. This means, the player can choose whether to go first or second in that Phase. At the start of the game, the player that deploys first Holds The Initiative for the first turn's movement phase, but the start of each subsequent phase requires a roll-off.

Every army has a Strategy Rating representing the ability to rapidly implement a successful plan throughout the scope of the battle (normally, I write rules based on a standard CAD, but some other variant is appreciated). Both players roll one d6 and add their Strategy Rating to the roll. The player that rolls higher now Holds The Initiative and can choose whether to go first or second for that phase. Should the roll-off result in a tie, the player that doesn't Hold the Initiative gains it instead.

=Strategy Ratings (Initial)=
Space Marines: Strategy Rating 3. Cato Sicarius grants +1 Strategy Rating for a turn.
Chaos: I...need to think of something clever.
Dark Eldar: Strategy Rating 2. +2 Strategy Rating on Turn 1, +1 Strategy Rating on Turn 2.
Eldar/Harlequins: Strategy Rating 2, +2 for Movement Phase
Orks: Strategy Rating 1, +2 Strategy during Waaagh, +2 Strategy Rating in Assault Phase.
Tau/Admech: Strategy Rating 2, -1 Strategy Rating for Assault Phase unless led by Farsight in which case it is +1.
Necrons: Strategy Rating 2. Zhandrekh gives Strategy Rating 3. Imotekh is Strategy Rating 4 unless fighting Orks (in which case he is Strategy 0).
Guard: Strategy Rating 1, +2 if led by Creed; may select a single phase each turn to have +2 Strategy Rating.
Tyranids: Strategy Rating = Turn Number. Swarmlord lets the player roll two dice and drop the lowest for the Strategy Rating roll.

Feedback and suggestions are appreciated of course.

Seems promising so far, I've played a few games where you alternate units, and that's how activation goes and it works rather well. Maybe for Chaos give them a base strategy rating of 2, and give them a +1 if their army is led by a chaos lord, maybe an additional +1 if their army includes Abbadon, or some other big special character.

Chaos is about scaring the crap out of you. Fear is pretty common and everything they bring or wield is overkill. In close combat, they are better than you or at least think so.

Definitely should get strategy bumps during Psychic Phase if you ever implement that. Otherwise they're just Space Marines and would probably be just as tactical, assuming they weren't disorganized.

Wouldn't want to force players to include different gods or daemons and troop-heavy choices are a thing still. However, a big thing with Chaos (and Daemons) is that sheer randomness of the Warp!

Therefore, I think it only makes sense for Chaos to have the following rule:

Chaos: Strategy Rating D6 - At the start of every turn, roll a D6. That's how sane your troops are this turn.

Wow, funny how close you are to my version of a phase-based game. I'm in the process of writing a new rulebook and I'll stick with my own ideas but these sure are interesting.