One (admittedly idealistic) solution would be to spread awareness of this dynamic and its toxicity. You can’t totally expunge it that way, but you could make it less prevalent (i.e. upper-middle managers probably can’t be saved, but it might get hard to find enough somewhat-competent lower-middle managers who will play along).
What would it look like to achieve an actually-meaningful level of awareness? I would say “there is a widely-known and negative-affect-laden term for the behavior of making strictly-worse choices to prove loyalty”.
Writing this, I realized that the central example of “negative-sum behavior to prove loyalty” is hazing. (I think some forms of hazing involve useful menial labor, but classic frat-style hazing is unpleasant for the pledges with no tangible benefit to anyone else). It seems conceivable to get the term self-hazing into circulation to describe cases like the one in OP, to the point that someone might notice when they’re being expected to self-haze and question whether they really want to go down that road.
Important update from reading the paper: Figure A3 (the objective and subjective outcomes chart) is biased against the cash-receiving groups and can’t be taken at face value. Getting money did not make everything worse. The authors recognize this; it’s why they say there was no effect on the objective outcomes (I previously thought they were just being cowards about the error bars).
The bias is from an attrition effect: basically, control-group members with bad outcomes disproportionately dropped out of the trial. Search for ‘attrition’ in the paper to see their discussion on this.
This doesn’t erase the study; the authors account for this and remain confident that the cash transfers didn’t have significant positive impacts. But they conclude that most or all of the apparent negative impacts are probably illusory.