Please explain why not doing so in this specific example would not be beneficial.

Allowing two students to swap would create incentives that will undermine the fairness of the system, thereby creating unfair situations a few years down the road. Highly educated parents and rich parents are more likely to complain, and by complaining they would be rewarded with a higher chance of their kid getting into a good school.

Schools are funded with public money, and getting into a good school should be equally achievable to everyone (regardless of the background of their parents). That's why swapping places was forbidden. It's about the system's integrity and the system's fairness, not about the individual outcomes.