Psychological safety is neither necessary nor sufficient to achieve our goal.
Historically, plenty of orgs have made significant contributions without much psychological safety. These tended to be more autocratic, command-and-control oriented. This approach worked well 50-100 years ago.
But in a VUCA world, psychological safety is ever more important, as speed, adaptive performance, and distributed creativity do appear necessary to succeed in making our intended contribution. And psych safety enhances those necessary ingredients.
Taking an autocratic path also puts more pressure on leaders to have all the right answers, since the team is not benefitting from the full voice and creative energy of team members.
So cultivating psych safety is a choice. It's not absolutely necessary. But damn, it does make everything better.
(For my fellow science geeks, I'm asserting that psychological safety moderates rather than mediates performance.)