Note that even if everyone were equally able to strategize, doing so would reduce efficiency: after all, to strategize students lie about their preferences, and

Note that even if everyone were equally able to strategize, doing so would reduce efficiency: after all, to strategize students lie about their preferences, and the lottery takes those lies into account. It's the garbage in; garbage out principle. Some of the stratgizing students will get into schools on their list they really only put there as a trading option. So it's not just about fairness; it's also about ensuring the algorithm works in the first place.