Curves of constant width are also the general answer to a brain teaser: "What shape can you make a manhole cover so that it cannot fall down through the hole?" In practice, there is no compelling reason to make manhole covers non-circular. Circles are easier to machine, and need not be rotated to a particular alignment in order to seal the hole.
So do interviewers really think that they are testing the applicant's mindset and problem solving skills by asking interview questions that were well-known and cliché five years ago, or are they just checking if you memorized a bunch of job interview trivia?
While it's true that yama is Japanese for mountain, and some mountains use such a suffix in their name, Mount Fuji is an exception because it's made of the shattered Touhous of the Nipponese. They would refer to it as Fuji-san, using a suffix normally reserved for addressing people.