I never have understood the appeal of the White Castle hamburger. It seems like a stripped down burger. A burger is not complete without lettuce, tomato and onion with a special 1000 Island sauce. Even the bun is funny. It seems like a dinner roll.
Originally they were very cheap (around 5¢, going up to 10¢ in the 1940s). They kinda kick-started the whole fast-food industry. For a company that started in Wichita KS, they certainly remain very popular in the New York City metro area; theyre affectionately known as ratburgers (versus the slider nickname in ads).
Perhaps people find the most frightening aspect of the patties to be the five-hole design (dating from 1949). The burgers are not flipped over when being cooked; the holes apparently facilitate this.