I'm pretty up of bike technology stuff and I'm not aware of any decent solid tires. If people would keep their tires pumped and don't ride them until the treads are showing not many flats will happen. I average maybe one flat a season and I ride 5,000+ miles. Usually it's a piece of glass.
When I am on a fenderless bicycle (I have manymmachines) I used my hand to groom the rolling tire quite reflexively. You are correct about how few flats you get with the right equipment and if you are careful. It takes glass slivers, thorns, and other sharp opjects a few rotations to breech the tire's integrity.
I get very few flats in the course of a year. I still use sewups on my racing bikes, now those are fun to patch.