What motivates a research mathematician to publish their work under a collective pseudonym? I can't imagine that something like that is good for one's career.
Fun, collective work and love of mathematics’ for mathematics’ sake?
The group also got its start in the 1930s, the current “publish or perish” mindset was decades away. And new subfields were still getting discovered left and right so there was no lack of material anyway.
Most if not all of them were university teachers in France and former students of ENS (so they already were civil servants before their career even started). Their careers weren't really at stake.
Most of the members had very impressive career anyway. Obviously there are no Fields medalist amongst the founders - they were already too old but I think something like five of the later members got it (Schwartz, Serre, Grothendieck, Connes and Yoccoz). There are probably more if we could count the current members.