everyone makes a sacrifice to optimize for a zero-sum competition, ends up with the same relative status, but worse absolute status.

I'm a bit surprised I haven't seen this particular incentives problem named in the academic literature.

Robert H. Frank has called it a "positional arms race". In a relatively recent article on higher education he gives this summary:

Participants in virtually all winner-take-all markets face strong incentives to invest in performance enhancement, thereby to increase their chances of coming out ahead. As in the classic military arms race, however, many such investments prove mutually offsetting in the end. When each nation spends more on bombs, the balance of power is no different than if none had spent more. Yet that fact alone provides no escape for individual participants. Countries may find it burdensome to spend a lot on bombs, but the alternative—to be less well-armed than their rivals—is even worse.

In light of the growing importance of rank in the education marketplace, universities face increasing pressure to bid for the various resources that facilitate the quest for high rank. These pressures have spawned a positional arms race that already has proved extremely costly, and promises to become more so.