He also appeared in an episode of I Spy as a character that was very much to my eye a prototype for Mudd.
Well that really was his specialty - playing blustering con men or comical authority types. Every actor has their signature bits and mannerisms. Carmel worked a LOT in the 60s, because he had an effective character type he could play.
It will be interesting to see in These Are the Voyages 2
, how difficult *ahem* expensive it was to get Carmel for the second Harry Mudd show - when they are writing a show specifically for a character you did, you most likely get a nice payday.