That's the incentive: CBC makes actual objective performance evaluation possible (i.e., performance evaluation for people and projects). And if a leader resists that? That's telling. It signals something about their leadership and the actual culture they're fostering. CBC is for leaders who claim to want meritocracy and are willing to prove it.
History gives us examples. Andy Grove at Intel famously institutionalized "constructive confrontation" and rigorous OKRs, explicitly binding executives, including himself, to objective measures of performance. It wasn't a loss of power; it was the foundation of Intel's execution culture and competitive edge.
CBC is cut from the same cloth. It doesn't magically enforce itself; it makes accountability legible, so leaders either live their stated values or reveal that they don't.