[GDB]

I don't think a connection to the war is necessary, it's just that like you said most are just excuses to bring in popular characters.

That said, they don't have to be divine.

Spoiler for List of non-divine Pseudo Servants in JPN:

Jeanne (in Apo, not in FGO), Zhuge Liang, Sima Yi, Muramasa, and Rasputin are all examples. If we don't include Jeanne, that's about a third of the pseudo servants in the game being non-divine.