Halverson's was popular through the years because it was "just a cozy place," she said. "Not like your chains that you have out there. People just enjoyed the supper club atmosphere because you don't have a whole lot of those out there anymore."
I feel like someone could write a long-form New Yorker article about just that "coziness". It's a defining characteristic of so many old sit-down places, and it comes in different flavors, depending on the type of establishment (diner vs. tavern), management's awareness of decor (deliberate effort vs. incidentally accumulated kitsch, for example), the evolution or non-evolution of the clientele, etc. The feelings I got when walking into Cypress and Fernwood were different yet the same.
Whether that's an endangered species, I'm not sure. Some atmospheres are surely generationally-specific, but perhaps others are not. While chains have grown in number and power, I'd think there would always be room for comfy destination restaurants.