American investors are increasingly acting on the realization that a broad-based indexing strategy is superior to investing in individual stocks or actively managed funds. That’s great news for investors, who will pay less and get better returns. But it has troubling implications for corporate governance.

No passive investor cares much about governance of a particular company. The impact on an index when a single company underperforms is usually either slight or offset by gains from its competitors. It may be rational for...