I recall reading somewhere, maybe in TMOST, that casting director Joe D'Agosta found himself being credited in the industry for very inventive casting -- when the truth was that he was just winging it, and didn't know better! William Campbell himself thought it was marvelous that a guy from the Bronx had a chance to play Trelane, a fop.
D'Agosta often did cast performers against type, for example eternal one-note bad guy Morgan Woodward as Simon Van Gelder, at the very least a complex portrayal. More casting trivia: T'Pau was played by Peter Lorre's ex-wife! My favorite unusual casting was Paul Fix, a verteran of countless Westerns, as Kirk's first chief medical officer. He had a very long career, later turning up on "The Rockford Files."
Belli's casting was unfortunate, but it was just stunt casting, just as Joe Piscopo was placed on TNG.
(Incidentally, it's well known that all Sikhs involved in the Eugenics War were beardless, long-haired Mexicans. That's why Marla and the rest all recognized him as Khan so easily.)