It’s difficult for me to imagine that permanently shading the roof and leaving an air gap above it would not improve things in addition to the presence of insulation and the attic itself, since it would lower temps in the attic even further. Regardless of the presence of insulation, reducing the delta between the attic temp and interior temp seems like it would be a win to me. My question, ultimately, is how much would a spaced layer above the roof impact this. To me, it feels like it would impact that delta a lot, but maybe not.

When you have an attic, you can go further by insulating the roof - this keeps the warm day air out, and during the night you can open windows to let the cool night air in. Historically roof insulation was done with thick layers of thatch, though light-weight synthetic alternatives are more common in modern construction. A well-insulated roof won’t let through any appreciable amount of heat.

Then as things get hotter, build the roof taller, allow for natural air flow to dissipate the heat, and finally put the building on stilts so air can flow under it.

Retrofitting existing buildings to have space for good insulation is expensive, especially with the atrocities the US has been building in suburbs for the past 80 years.

(None of this is to disagree with the idea of using lighter/more reflective roofing materials, FWIW.)

Edit - and I don’t mean a giant umbrella or similar, I feel like a typical home could easily just have a structure the size of the roof and spaced a few inches out from it.

Would that help the larger city climate? Well sure, if it’s trees. A giant umbrella over the top of a skyscraper? Who knows