Always happy to toss my two cents in.
INIT ON CHARACTER LEVEL:
I'm still not completely clear on what the core suggestion here is. Are you...
A.) Proposing that players use the highest initiative value in their entire army to determine who has the highest/lowest initiative, then have the player with the highest/lowest initiative do all their actions for that phase before allowing their opponent to do all their actions for that phase. So for instance, my keeper of secrets has a really high initiative, so I'll generally have the highest initiative on the table. In my Psychic phase, I'll end up casting all the psychic powers known by all my psykers (not just the keeper of secrets), and then my opponent will get a chance to cast with all of his psykers.
If this is correct, you end up with weird scenarios where a chaos army full of cultists (initiative 3) but lead by a Keeper of Secrets (initiative 9? 10?) well have a higher initiative overall than an army of eldar (initiative 5, 6, and occasionally 7).
B.) Proposing that units take turns on a unit-by-unit basis, using their initiative stats to determine the activation order. So in the psychic phase, all Initiative 5 units would take turns activating, then all initiative 4, then all initiative 3. Then in the movement phase, you'd start with the lowest initiative units (3), and take turns activating progressively higher initiative units.
Note that in this system, a player could potentially have both the highest and lowest initiatives. See above about the keeper of secrets + cultsts army.
WARLORD TRAITS/OTHER ABILITIES
TO BOOST INITIATIVE
You *could* give 'crons, orks, tau, etc. various bonuses to offset this inherent disadvantage, but you'd presumably be paying some sort of price for doing so. If you have a warlord trait that fixes the problems this turn system creates, for instance, you'd basically be saying that these armies have to take that particular warlord trait instead of something else just to break even. If you give various units/characters some sort of special rule to off-set the disadvantage, then you'd either have to raise the price of those units to reflect this new ability or else give to them for free. And if you're giving people a way to get around this new disadvantage for free, you probably shouldn't inflict the disadvantage in the first place.
PHASES GIVING ADVANTAGES
"For the phases, doesnt that happen now too. Player who goes first gets to fire off their spells? "
Yes, but I'd argue that your system, as I understand it, kind of makes the problem even more severe.
Let's say my army has a lower initiative than yours. In the system you've proposed (if I understand it correctly), I will...
*Not be able to use psychic powers until after my opponent does.
*Have to move my units before my opponent does, thus allowing my opponent to put his units in the perfect position to beat me up or run away now that he knows where all of my guys are.
*I'll get shot up by units that have moved to their ideal spots before I have a chance to damage my opponent at all.
*I'll get to declare charges or run before my opponent does. The latter could be useful as it might let me run away from an enemy that wants to charge me. The former is a lot less important because in your system, charging doesn't mean that I get to automatically swing first. Some dark eldar wyches, for instance, would be swinging before tactical marines regardless of who charged whom.
So basically, the assault phase is the only phase where the low intiative army gets any advantage at all, and that's kind of a meh advantage. In the official rules, it's true that going first lets you take some shots, toss up some buffs, and maybe get lucky and manage an assault before the player that goes second, but the player that goes second then gets a chance to realiate and make their actions count. Under the system you've proposed, it looks to me like the guy with the lower initiative just gets screwed over in every phase of the turn. :(
Or maybe I'm misunderstanding your proposal?