Here's a tropical house with multiple roof layers to stay cool: https://www.notechmagazine.com/2013/09/a-passively-cooled-ho...
https://wattsupwiththat.com/2012/09/12/something-practical-n... or the paper: http://callippe.com/blog/wp-content/uploads/2012/09/ORNL_roo...
But in any case... The overall reduction in energy use was about 5% better than calculated. The article stated that this was discovered to be due to the improved airflow between the roof and panels. Because the panels are installed 40mm-50mm above the roof, they leave effectively a narrow wind tunnel between themselves and the roof surface. This means that with the panels heating up, they cause an increased airflow over the roof.
This increased flow, in addition to the panels heating up instead of the roof, was enough to further reduce the energy required to cool the house down.
You must have been experiencing the same effect.
Here's a pic with the louvres open.
https://www.archdaily.com/255208/burton-barr-central-library...
Rooftop decks being so popular now, I expect someone clever will eventually add solar panels as shades.
So the idea is already there and makes sense; it's just a matter of time for it to be adopted on the consumer home market I suppose.
Now - if they would just manufacture homes to also suit the climate, and/or position them to stay cooler in the summer and warmer in the winter, etc.
Had the dome style of home taken off, especially here in Phoenix, things would be much better, because the roof wouldn't get nearly as much sun hitting it directly as standard ranch-style homes and others currently do. Monolithic dome construction, coupled with a mostly below-grade first floor, would do wonders for heating and cooling (I know of a house almost like that up in the New River area). Add in a solar chimney with evap cooling (Boyce Thompson Arboretum used to have a demo system like this), and you'd limit AC/heatpump usage to probably 1-2 months a year.
I wish I had the money to build such a home on a decent size plot of land somewhere, but I doubt I ever will.
The thing that surprised us the most when we installed our home solar system was how much cooler the house was during the summer, just because of how much the air-gapped panels on the roof reduced the heating load on the house. We noticed a significant reduction in our AC bills during the couple of months we had the system installed, but couldn't use the power due to permit-waiting.