Q: I understand why we pray for the pope and the local bishop. But why the separation of the clergy and the rest of the bishops from everyone else? Isn’t this separation left from the days of social class distinction?
A: Even Vatican II’s Constitution on the Church (Lumen Gentium) noted the distinctions in the hierarchy and the role of the laity, though it did so after it treated “The People of God” as a whole. That said, we probably don’t absolutely have to pray for people in hierarchical order. I’m not sure why they kept it. Maybe it was one way they could get bishops to agree to vote for more eucharistic prayers.