It's true that hire and tenure decisions are under the institution's control. But a lot of funding comes from external sources, and most public funding uses some sort of publication-based metric. There are exceptions, but that's the game. The CV of your PhD's is often judged by the publication list and the corresponding citations. That's research institutes where they might go, other universities, large companies etc. will look at this. It's difficult to change this system as isolated player, and coordinates efforts so far failed on the "what else" question.

A problem with the public sector in this instance is it has money to spend, but no way of allocating it particularly well.

It will just pick the best allocation metric it has available, even if that metric would never stand up to scrutiny in the private sector, or any more directly measured domain, public or private.