Do you know why bathroom stall walls don't go all the way to the floor? It's so the janitor can quickly mop out each stall, without needing to get down and scrub out the corners that would be created if the walls met the floor.
Custodian-based design extends to furniture, too. If you look at old card catalogs, you'll see the wooden legs are almost always tapered, and raised off the ground on metal feet. The tapers make it easier to mop around while minimizing the amount of wet mop contacting the wooden legs, and they're on metal feet so the water from the floor doesn't wick up into the endgrain of the legs. (The one below is on carpet, but you get the idea.)
It's a weird design for a kitchen, for sure; perhaps the original owner was a sports coach who routinely had the entire team and coaching staff over for breakfast. In any case, I guess what people didn't realize is that the seats are, of course, designed to pull out and swivel. I poked around a bit, and I'm pretty sure these seats are from Utah-based Seating Innovations. Here's what they offer:
The seats have a spring return that brings them back under the surface:
As for strength, the seats are not suspended from beneath the counter. As the company explains:
"The suspended seating system is freestanding and mounts directly to the floor. The cantilever frame system is typically concealed behind the finish panel and underneath the footrest, thus giving the illusion of chairs hanging from the countertop."
I wanted to see what the frames looked like, and found this time-lapse of an installation where you can get a good look at them. They look to be steel and are pretty beefy square tube stock:
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While I personally don't like the idea of seating that has a fixed range of positions, I can see the appeal for neat freaks who are constantly vacuuming or sweeping. It's a long way to go, but my guess is the customers in that category won't want to go back to conventional chairs.