So in addition to large-team leadership skills, there may be some niche technology/systems that only a limited number people have experience with multiple 1-3 year cycles of designing, building, maintaining, and replacing these uniquely large infra systems.
One other thought from your comment, which has been beaten to death, is the legacy product problem for Google, which is not going to magically go away. For people on the bleeding edge they just don't want to have another meeting where someone brings up, for instance, search. You don't have to worry about legacy products at Anthropic and OpenAI because none exist so it's certainly more greenfield.