What you describe is still a problem with the institutions, because it is ultimately the institutions that provide the incentives (in the form of jobs). You're right that they're using bad metrics, but it is the institutions who are making those bad decisions based on the bad metrics.

There are lots of better things, like people making hiring and firing decisions based on their evaluation of the content of papers they have actually read, instead of just a number. If someone is publishing so many papers that a hiring committee can't even read a meaningful fraction of them, that should be a red flag in itself, rather than a green one.

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.