Then you're back to trawling through every instance just to see whose turn to think it is, when you could just as easily already know.
True, but the actual loop through every character isn't the problem. As long as you aren't calculating the time-consuming AI every frame (the LinePicks in particular) then that's what's important.
Besides, with my approach you get a lot more flexibility. For example, it's trivial to adjust their reaction time; just adjust how long between updates.