You need audits and Blind-like channels to augment self reports.
Anonymous, third-party outlets for complaints like Blind can also likely be useful. Even at companies that never punish anyone for criticizing the company, participation rates in internal surveys are typically atrociously low, and people stop speaking up even informally if it's clear to them that nobody actually acts on employee feedback. Most companies probably perceive such channels of communication as threats, though.
Idk about audits. I worry that it's easy for them to become their own circus and overhead without materially improving things. But you may be right.