Is there another ICM strategy for shoving/calling which favors callers more?

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Is there another ICM strategy for shoving/calling which favors callers more?

This has been something I've been wondering for 10+ years at this point and I wanted to come back and ask now. Understanding of the game has advanced a lot so I figured someone might have an easy answer for me.

Super simple situation: SB and BB have small stacks, ICM considerations make them both strongly disinclined to get that money in.

My understanding of this situation is that SB has a very strong shoving spot because BB can't call very wide - it would be an ICM mistake even with some relatively good hands. So that's the equilibrium we play; SB shoves a lot, BB folds most of the time. This is an equilibrium, it results in SB winning a good amount of bbs and BB folding lots of hands. It's an equilibrium because neither player, on their own, can change behavior to improve their results.

What about if BB expanded their calling range though? BB could call with a tremendous number of hands if desired here. Now all of a sudden SB doesn't get to jam as often and (unless I'm way off?) this ends up being more profitable for BB because the ICM considerations that used to be stopping BB from calling now stop SB from shoving (once SB understands that BB has a wide calling range).

If there are four possible situations:
1) SB shoves a lot, BB folds a lot
2) SB shoves a lot, BB calls a lot
3) SB shoves a little, BB calls a lot
4) SB shoves a little, BB folds a lot

It seems like:
#1 is standard, equilibrium, best for SB, somewhat good for both.
#2 is nonstandard, nonequilibrium, and terrible for both SB and BB. HOWEVER the only way SB can adjust from it is to move to...
#3, which is good for BB and somewhat good for both. SB cannot improve their outcome from this strategy, but BB could by moving to...
#4, which is best for BB, somewhat good for both, but now SB can improve their own fate by increasing jamming frequency.

("somewhat good for both" just means the money isn't going in too often).

So basically I don't get why people who play tournaments regularly against each other don't establish #3, since I'm pretty sure there are ICM situations where BBs establishing #3 improves their profit.

I also just find the whole theoretical discussion surrounding this really weird, which is why I keep on coming back to thinking about it. BB could, at any time, stop calling as wide and start profiting more without SB catching on immediately. SB could, if they wanted, just go scorched earth and keep jamming wide even though BB was calling wide, which would be terrible for both players and could maybe force BB to stop calling wide. A pair who ended up in #3 strategy space would be playing a non-equilibrium strategy which had a better BB outcome than BB's outcome in an equilibrium strategy because ICM burdens were placed on SB in the non-equilibrium instead of BB in the equilibrium. Etc.

Anyway. Did anyone write a book or make a video which explains this all yet? Let me know please xD.

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