They need something they can check easily so the team can get back to work. It's hard to find metrics that are both meaningful to the business and track with the work being asked of the team.
You can look at revenue and decide "hey, we have a problem here" and go research what's causing the problem. That's a perfectly valid used for a KPI.
You can do some change by something like the Toyota process, saying "we will improve X", make the change, and track X out to see if you must revert or keep it. That is another perfectly valid use for a KPI.
What you can't do is use them to judge people.
Its easy to fake one metric, it harder to consistenly paly around 100 of them.
(But then it’s no longer KPIs probably, as one looking at the data needs to recognise that details and nuance are important)
Do you have enough KPIs that you can be sure that these targets also serve as useful metrics for the org as a whole? Do you randomize the assignment every quarter?
As I talk through this ... have you considered keeping some "hidden KPIs"?
can't say what the deep idea in this case is per se (haha (maybe the other commenter can shed light on that part)), but i guess if you have enough KPIs to be able to rotate them you have yourself a perpetual motion machine of the same nature as the one that some genius carried down from the mountain on stone tablets that we can sustain maximum velocity ad infinitum by splitting our work into two week chunks and calling them "sprints"... why haven't marathoners thought of this? (h/t Rich Hickey, the source of that amazing joke that i butcher here)
maybe consciousness itself is nothing more than the brain managing to optimize all of its KPIs at the same time.
A 90 day target is questionable, but regularly changing the metrics are a good way to keep people from gaming them.