I'm now wondering if painting a roof white is better than covering the same roof with solar panels and using that to drive air conditioning (in the house). My intuition is that painting it white must be vastly more environmentally friendly, although it probably doesn't reduce the temperature very much compared to aircon.
AC doesn't make it cool it merely transfers the heat to the outside in an energy efficient manor. The emerging tech is special coatings that convert heat to an infrared frequency that easily escapes the Earth's atmosphere.
In cooler climates, you are now taking a hit on heating costs. That now blocked Winter sun would have provided some amount of free warmth.
Sure, but the physics still cuts both ways. Either sun hitting the roof causes measurable heating or it does not. The temperature gradient must flow.
Sun heating in Winter = awesome. Sun heating in Summer != awesome.
I am not arguing the strength of the effect, only that you must account for all seasons.
There are certain materials that aren't just white but also specifically radiate heavily in IR bands that the atmosphere is particularly transparent to and so can actually stay sub-ambient temperature while in sunlight. See, for example, https://onlinelibrary.wiley.com/doi/full/10.1002/eom2.12284
But adding conventional AC is never going to cool down the world.