With respect, I think that's wrong.
If all parents agree that school A is better than B, but parent 1 cares much more about A>B than parent 2 does, then the sum-of-utilities is different (so, not "zero sum") depending on whether [ 1→A; 2→B ] or [ 1→B; 2→A ]. Every change in outcomes leads to someone losing (compared to the counterfactual), but the payoffs aren't zero-sum.
That example is kind of useless, but if you have three parents and three schools (and even if parents agree on order), but each of the parents care about A>B and B>C in different ratios, then you can use that fact to engineer a lottery where all three parents are better off than if you assigned them to schools uniformly at random. (Sketch of construction: Start with equal probabilities, and let parents trade some percentage of "upgrade C to B" for some (different?) percentage of "upgrade B to A" with each other. If they have different ratios of their A>B and B>C preferences, positive-sum trades exist.)
Then, in theory, a set of parents cooperating could implement this lottery on their own and agree to apply just to their lottery-assigned school, and if they don't defect in the prisoners' dilemma then they all benefit. Not zero-sum.
Of course, it can also be the case that they value different schools different amounts and a bad mechanism can lead to an inefficient allocation (where pairs would just be better off switching), and I could construct such an example if this margin weren't too narrow to contain it.
It is separately the case that if the administrators have meta-preferences over what parents' preferences get satisfied, then they can make a choice of mechanisms ("play the metagame", as you put it) that give better / worse / differently-distributed results with respect to their meta-preferences.
While the zero-sum nature is unavoidable
I believe this is false as stated:
While 'zero-sum' is correct in a loose colloquial sense that at least one person has to lose something for any group to improve, I think it's actually important to realize that there are mechanisms that improve overall welfare -- and so the system administrators should be trying to find them!
You cite the Gale-Shapley papers, but are you aware that the school-choice mechanism you described is called the "Boston mechanism" in the field of mechanism design? Because, well, it was also the system in place at Boston Public Schools (until the early 2000s, when they changed to a Gale-Shapley algorithm).
Pathak and Sonmez (2008) is the usual citation on the topic, and they find (as you suggest) that the change makes the most "sophisticated" parent-players worse off, but the least-sophisticated better off.
Think of it as your own little lesson in irreversible consequences of appealing actions, maybe? Rather than a fully-realistic element.
My guess would be that a commitment to retaliation -- including one that you don't manage to announce to General Logoff before they log off -- is positive, not negative, to one's reputation around these here parts. Sophisticated decision theories have been popular for fifteen years, and "I retaliate to defection even when it's costly to me and negative-net-welfare" reads to me as sophisticated, not shameworthy.
If a general of mine reads a blind commitment by General Logoff on the other side and does nuke back, I'll think positively of them-and-all-my-generals. (Note: if they fire without seeing such a commitment, I'll think negatively of them-and-all-my-generals, and update on whether I want them as collaborators in projects going forward.)
Grumble grumble unilateralists' curse...
The charger was marked 150kWh, but my understanding is the best the Bolt can do, in ideal conditions with a battery below 50%, is 53kW. And the 23kWh I saw is about typical for a Bolt getting to 75%
I think that this paragraph should say "kW" instead of "kWh" both times? Either that, or I've misunderstood what you're trying to communicate.
It might!
In case it would also help to have two-to-three Harvard and/or MIT professors who work on exactly this topic to write supporting letters or talk with your school board, I'll bet money at $1:$1 that I could arrange that. Or I'll give emails and a warm intro for free.