They decided that everything they produced should be a group effort and not the work of any particular individual. How else could it be a unified theory reflecting the best of mathematical knowledge at the time and not the opinions of one person? So the mathematicians created a fictional persona to whom they attributed their work: Nicolas Bourbaki* of Poldevia. They took pains to make him seem like a real person.8 Many of the students who used their textbook never had any idea that Bourbaki was a group.
Optimises for long term thinking and reduces 'returm on politics'. A bit like blank firing squads, ensures everyone is equally responsible and not responsible for the outcome. Hypothesis: this increases psychological safety, and probably innovation.