It's not important to Sigil, but it's the skeletal structure the Outer Planes are built on and a fair amount really don't have a theme to them at all without their alignment identity. Mechanus is the Lawful Neutral Plane, if Mechanus isn't about Lawfulness, then what is its theme?
There are even more dependant upon alightment for identity planes, like Arcadia and Biopotia, without alignment they are extremely boring and have no identity at all. The more Chaotic Good planes don't suffer nearly as much from this as they draw deeply from Mythological roots more (really only Mount Celestial aka Heaven really seems to have a sold flavour Lawful God wise), but Aborea becomes Greece's Feywild, Beastlands become Lion's Safari, and Ysgard become Viking Village.