Consider people who buy concert tickets and immediately resell them at higher than retail prices. I don't personally object to that, but I note that it makes a lot of people angry. It's not terribly clear that it makes things "better globally, by definition" either. The same number of people get to attend the concert with or without resellers. The band and the venue don't get any more money with resellers in play. The only set of people really better off are the resellers, who strategically mimic interest in attending but immediately trade their dozens of tickets for more money. That's a very narrow, rather than global, improvement from strategic trading.

The same possible dynamic with schools is, according to the article, one reason school trades aren't allowed. Strategizing traders could mimic interest in attending popular school X, but really intend to trade a school X place for their true preference later. Everyone who isn't strategizing that way is worse-off or no-better-off when the strategic behavior is allowed.

Note that more complex rules with more potential for strategizing don't just inconvenience individuals. More complex tax codes or regulatory codes, too, tend to disadvantage e.g. small businesses that can't afford legal teams to strategically take advantage of non-obvious consequences of the rules. The small businesses aren't "envious" that bigger ones have a higher laywer-to-engineer ratio. Small business employees aren't necessarily any more foolish than big-co employees, except in specific matters of legal interpretation and strategizing. They just want less exploitable rules so that facially-optimal and actually-optimal behaviors stay closer to each other.