What you are describing with your risk/reward scenario is still math. And the gap doesn't need to be huge. It needs to be anything. You can prove which is more likely and then you should do the more likely.
But, EVEN IF we were to say you are 100% correct (which I am not) what this always boils down to in these discussions is people on your side of the argument have to present rare specific scenarios in order to say "See! What about now! Doesn't the game have interesting choices now!" But if the game only gains these interesting choices in these rare specific scenarios then how often do they come up in a game? Of your # of units * number of phases they act in decision points what % of them are these specific situations that are interesting (which again, I am not agreeing with you that the one you present is that) ?
Lets figure out some variables. If we are talking about having say... 12 units in an army. They all move, 3 are psykers, lets say 10 can shoot, and 9 can melee.
Thats 34 simplified decision points turn 1 player 1. Not accounting for player unit losses, (34 * 6) * 2 = 408 basic decision points in a game.
How often is your specific scenario coming about? Once a turn? Twice? Lets call it 5 because I am feeling crazy generous. 60 decision points out of 408. It's just over 14%. Again. 5 a turn is me being SUPER generous. Lets remember that turn 1 is basically just auto pilot. NONE of these scenarios are showing up then. And judging by this thread (
https://www.dakkadakka.com/dakkaforum/posts/list/801802.page) these decisions might spike in turn 2 and then decrease each turn after with turn 3 and 4 being increasing odds of the game being a foregone conclusion.
So even my super generous 5 a turn is probably more likely 0 turn 1, 5 turn 2, 4, 3, 2, 1. 30 a game. Not 60. or 7% of all decisions.
So based on the debatable and highly faulty idea that your scenario isn't just math with an optimal solution, and my generous idea that that scenario arrives regularly throughout the game, it still makes up less than 10% of all game play. Great.
I see what you are doing trying to come up with terms like the illusion of power to counter the concept of the illusion of choice. I even appreciate it to an extent.
But no. The illusion of choice is an ACTUAL thing. It's studied. It's understood. The designers of WoW talked about how the old talent trees were a bad mechanic because they created a lot of illusion of choice which is why they ditched them.
"Illusion of power" is nonsensical.
When a turn is interrupted you have to be able to predict what the other player is going to do. People are different from mechanics because they can be tricked. They have agency. The moment the calculation is trying to think what would that guy do instead of what are the mechanics going to be you enter into an entirely different set of circumstances.