Is there white slate?
If there is white tile, which is manufactured, there can be a coating for slate to make it cooler than dark slate. The covering has to be fire PROOF to continue the protection of the slate alone.
There should be other stone tried in testing laboratories as well. Granite comes in many colors, etc. There are good alternatives for building energy efficient buildings. There is no reason for the USA to lag behind other countries that are finding real solutions to their GHG emissions. It is vital we do. Generations to come need to know we believed in their lives and achievements that are benevolent and not self-serving.
The California slate roof worked to protect the home because the wind blown embers could not find a place to start burning. Imagine the difference between a tar roof and a slate roof.
What does saving energy dollars tell us about white roofs? It tells us there is 25% less HEAT absorbed by the building that has to be compensated. I think most people would agree 25% less energy use is a good thing. Now, place that white roof at the two caps of Earth. How much HEAT energy is reflected back to space. It is a lot. It is important to maintain coolness of Earth. Everyone can help. End emissions of GHG. It is important.