Having long ago participated in "harvesting" stone crab claws, and years later paid too much for them at Joe's in Miami, the "big name" place which popularized them to almost "cult" status, I've since chracterized them as "Rich Man's Rock Shrimp", an altogether too little appreciated treat from the sea, rarely seen on menus.
If they weren't so messy and so much trouble to eat the old "Barbecued' (read Cajun seasoned and deep fried) blue crab found at backroad places like Satain's in Sabine Pass have similar appeal, but remain in almost cult status like the "Chili Crab" of Singapore and Malaysia, little known beyond the small segment of diners exposed to their excellence.
For me, the "Good Old Days" on the Gulf Coast came with a package of chicken backs left out overnight to age to aromatic state, a piece of twine, and a dip net, a sport at which even my non-angler kid sisters could master and help fill a pot. A mess of boiled crabs, some newspaper, cases of cold beer, and time, lots of time, made for a liesurely beach dinner and good conversation while cracking and picking.