So we're trying to prove "mathematically" that the K-shaped economy is "rational", and trying to circumvent the fact that the mathematical rules of economics depend on the social, political, and behavioural substrate by which those rules derive their efficacy.
Which is fine if nobody has agency, politics is irrelevant, and we just accept everything we're told at face value if it's framed in sufficiently mathematical language.
As much as you may want to move from the low to high equilibrium, it would be pretty hard in an ancient society. In the modern world, with enough exuberance, it seems much easier.
Because we definitely seem to be in a world where GDP inflation is getting more and more divorced from incentives to actually produce things.
With respect to AI and the paper being discussed specifically, all evidence I've seen is that AI's primary applications are within military and intelligence and that the escalating arms race in those domains is actively undermining things that people would generally like to see being produced (food and housing specifically are illustrative here).
Notably, one of the reasons that the military industrial complex can be hard to unwind is that it works well for capital and workers. Consider all the programs you've heard of which boast about providing jobs in every single state. Whether these different equilibria are better or worse for labour (or fractions of labour giving you your diverging K-shape) is a separate question and potentially changes over time.
One historical event you could model as a change in equilibria was the industrial revolution. Instead of elites consuming economic surpluses, the economy change into a mode where those surpluses could be reinvested in productive capital, new technology, and manufacturing in a self-reinforcing cycle (of course these avenues didn't really exist before). Famously, within this new equilibria, labour did not do well at first; awful conditions in factories with terrible life expectancies. But those workers' grandchildren lived lives of relative prosperity as a result.
All of which is to say, the existence and description of multiple equilibria in economies is a different question from how labour and capital fare in those equilibria.
So you have it exactly backwards: the K-shaped economy refers to the continued rise of asset valuations as workers real wages decrease.
But I'm not going to keep arguing with you since you seem to be afflicted by "Math brain" (defined here by the belief in homo-economicus where humans can be accurately modelled as a selfish calculator - and please don't correct me on the calculator metaphor, I'm being hyperbolic).
Let's take what we do know from AI and cognitive science seriously: if we accept that humans are some sort of biological prediction machine, that doesn't give us a completely predictive model. There's a sort of "measurement problem" when it comes to self-prediction: while the goal of environmental prediction is clearly accuracy, the goal of self-prediction cannot be accuracy since self-prediction is inherently accurate by virtue of the actualisation of self-predictions. What then discriminates within the self-predictive model between multiple actualizable self-predictions?
If Math-brained believers in homo-economicus are to be believed, then human behaviour is completely determined by what basically amounts to greed. Certainly that's what generally selects for those who occupy positions of power and prestige in our society, and thus based on current political norms has turned into a somewhat self-fulfilling prophecy.
In this since Nietzsche was right: "God is dead." He was killed by enlightenment thinking and replaced with rational self-interested agents governed by predictable macro-economic models... which keep being wrong, because humans are not universally greedy and behaviour, politics, and psychology actually matter a great deal. (Nor is the new god of "rational" selfishly motivated acquisition, expansion, and power-seeking really that new of an invention - he is sometimes called "Moloch", and is in fact perhaps the oldest God, and humans keep discovering he's a pretty shitty God to worship; I have no doubt that he will prove equally destructive and unkind to us if we insist on continuing to and/or reverting to worshipping him dressed up in "rational" mathematical economic language).
And the K in K shaped economy came from turning the K 90 degrees so that the left arm (representing the low wage service sector) and the right arm (representing rising asset prices) were elevated while the middle was depressed. It got retconned to mean "increasing inequality" by those who couldn't bear to admit that something had gotten better for those lower on the wage scale (which objectively happened back then).